Decision-Making in Simultaneous Games: Reviewing the Past for the Future

Transcription

1 University of Massachusetts Boston From the SelectedWorks of Mohsen Ahmadian Winter December 8, 2017 Decision-Making in Simultaneous Games: Reviewing the Past for the Future Mohsen Ahmadian, University of Massachusetts Boston Ehsan Elahi, University of Massachusetts Boston Roger Blake, University of Massachusetts Boston Available at:

2 Decision-Making in Simultaneous Games: Reviewing the Past for the Future Mohsen Ahmadian University of Massachusetts, Boston Ehsan Elahi University of Massachusetts, Boston Roger Blake University of Massachusetts, Boston December 8, 2017 Abstract This research reviews the prior behavioral economics studies in simultaneous games and behavioral operations management literature to propose some new research avenues in the field of behavioral operations management with a focus on simultaneous competitions. Findings of this study show that although many behavioral studies have been done, behavioral research on simultaneous competitions in operations management is rare. Review of the literature indicates that some contemporary trends are emerging in behavioral studies, so there are many opportunities for future research in this area. Moreover, this research highlights the importance of decision science as an interdisciplinary field of study, which in turn emphasizes exploring other disciplines to enrich the behavioral decision-making literature and developing more comprehensive and meticulous behavioral theories. Keywords: Decision-Making, Behavioral Operations Management, Behavioral Economics, Simultaneous Game 1. Introduction For many years research in economics was based on three main assumptions: (1) Players care only about their profits; (2) Players are able to optimize and make no optimization errors; and (3) All information is available to all players (Katok and Pavlov 2013) and therefore decision-makers always choose the best option (optimal solution). This assumption was violated in some studies, and an increasing amount of research has reported that decisions in practice are not as predicted theoretically. Accordingly, researchers started investigating these observations, and several models and theories have been developed to explain what happens in reality. How real decisions are made is the focus of research in psychology and decision science contrary to the normative research that examines what a decision-maker should rationally do (Loch and Wu 2007). Studying human behavior helps not only to better understand how people make their decisions Page 1 of 27

3 but also to learn how to overcome behavioral biases and make better decisions. Nowadays behavioral decision-making is a well-established research area for studying human issues in many disciplines and is used in many business disciplines. Economics is one of these disciplines which have employed behavioral models and theories. The experimental economics field has seen exponential growth every decade since Through this evolution, the focus of experiments has expanded to include an emphasis on developing a new behavioral theory to explain gaps between established economic theory and experimental results (Bendoly et al. 2006, p. 739). Some review studies have been done in this area (e.g. Ho et al. 2006, Goldfarb et al. 2012, Dechenaux et al. 2015). Review of this literature shows that although many theories and models have been developed to explain individuals' behavior, none of them can do it completely. Therefore, there are many opportunities to develop new theoretical models, new laboratory experiments, and new field applications to shed light on human behavior. In recent years, behavioral studies have been brought to operations management (OM) field where many different decisions are made in enormous types of problems, and a various range of decision errors are observed in practice. Behavioral operations management (BOM) research explores the theoretical and practical implications of incorporating behavioral and cognitive factors into operations models to understand how OM decisions are made in reality, and how different behavioral factors affect them. Although the study of behavioral issues is new in OM, many researches have adopted a behavioral operations perspective, and BOM is going to be enriched. Review of behavioral studies in OM can be found in Bendoly et al. (2006), Loch and Wu (2007), Gino and Pisano (2008), Wachtel and Dexter (2010), and Kundu et al. (2015). Many of these studies are based on newsvendor problem, in which the main challenge is matching the supply (order quantity) with the uncertain demand. In the business world, decision-makers are faced with far more complicated situations. For instance, there is usually more than one retailer in a supply chain. These retailers and their fulfilled order quantities are not independent of each other. Therefore, retailers deal with a more complicated problem and compete for a higher payoff. Besides the retailers competition, suppliers competition is another scenario that the extensive literature in multi-sourcing indicates its importance (see Minner 2003 and Yao and Minner 2017 for a detailed review). Hence, simultaneous game is a more realistic scenario in many real-life situations. The study of this type of game can be worthwhile in its broad applications and being closer to what happens in practice. Simultaneous competitions have been studied in many behavioral studies in the economics literature, however, studies of this type are rare in BOM. In this paper, we aim to review the relevant articles in the literature to find the behavioral factors and cognitive biases that can explain the people s behavior in the simultaneous decisionmaking process. For this purpose, we focus on the behavioral economics and BOM literature. Among the vast and well-developed literature of the behavioral economics, the experimental research of economic contests and games is one of the relevant ones to OM research area, and we focus on just simultaneous competitions which is the goal of this study. In most of these studies, researchers aim to find whether subjects behavior is consistent with the theoretical prediction, and if there is a deviation, try to explain it from behavioral aspects. Studying people s behaviors, finding some behavioral factors and cognitive biases which can affect decisions/decision-making process, and explaining the results based on these factors is one of the interesting streams in behavioral studies. Reviewing the literature helps us to find these behavioral factors and cognitive biases, and be familiar with various behavioral models and theories which are developed to Page 2 of 27

4 describe people s observed behaviors. Accordingly, richer and more realistic models can be developed which can help managers and decision-makers, at least, in two ways. First, decisionmakers will be aware of these factors and biases, and they can make more precise and rational decisions by avoiding or eliminating them. As an example, in decision-making and risk management literature, Montibeller and Winterfeldt (2015) study the cognitive and motivational biases that are relevant to decision and risk analysis and provide guidance about the existing debiasing techniques to overcome these biases. Second, decision-makers and managers can better know other parties (e.g. customers, personnel, competitors, partners, suppliers) and perhaps predict their actions and decisions more accurately, and in this way, they are able to adjust their decisions. From theoretical perspective, this paper helps researchers to explore the gaps in prior studies, and design new research in BOM to develop more realistic theories and models, as Bendoly et al. (2006, p. 737) state Many of our techniques and theories ignore important characteristics of real systems and therefore are perceived to be difficult to apply in practice. [ ] A common factor in this breakdown is people. When it comes to implementation, the success of operations management tools and techniques, and the accuracy of its theories rely heavily on our understanding of human behavior. This paper continues in Section 2 with an explanation of the simultaneous games and a brief review of the prior studies in this area. Section 3 reviews the related literature in behavioral economics and BOM and explains the identified behavioral factors in prior studies. Moreover, it briefly discusses relevant papers and their findings and, based on them, proposes some recommendations for future research in BOM literature, especially in simultaneous games. Finally, section 4 summarizes major contributions of this study as conclusions. 2. Simultaneous Games The simultaneous game, in game theory, is a game where all the players move simultaneously, or if they do not move simultaneously, no player is aware of the earlier players' actions. Indeed, in simultaneous games, each player chooses his/her action without knowledge of the actions chosen by other players, and the decisions are made based on what each thinks the others will do. Outsourcing decisions, pricing, and marketing some new product, mergers and acquisitions competition, voting and political decisions could be some examples of this game. What differentiates simultaneous games from sequential games is that players in a simultaneous game must think not only about their own best strategic choice but also the best strategic choice of the other players. This type of game is a more realistic scenario in many real-life games, so the study of this type of game helps us to better understand how people behave when they are making their decisions in a situation close to what happens in reality. Research in this area helps researchers to examine people s behavior more broadly and explore new aspects of it. In other words, how people make their decisions in a more realistic scenario could be realized in more detail, which helps researchers to develop more applicable and better predictive models. Findings of these studies, in addition to the theoretical implications, will give the practitioners the opportunity of improving their performances by not only avoiding behavioral biases in their decisions but also knowing more about other parties and their behaviors. In recent decades, simultaneous games have been studied in behavioral economics literature in some contexts such as auction theory (e.g. Davis and Reilly 1998, Goeree et al. 2002, Rapoport and Amaldoss 2004, Gneezy and Smorodinsky 2006, Engelbrecht-Wiggans and Katok 2007, 2008 & 2009, Lugovskyy et al 2010), Page 3 of 27

5 and rent-seeking (e.g. Milner and Pratt 1991, Davis and Reilly 1998, Potters et al. 1998, Parco et al. 2005, Sheremeta 2010, Lim et al. 2014). The rent-seeking game was first modeled by Tullock (1980) and in which contestants compete to win a prize (rent). The amount of the contestants expenditure increases the probability of winning the prize. This expenditure is just spent to increase the chance of winning the rent and usually does not create any real value, and its total value, under certain conditions, could equal the value of the rent (rent dissipation). The probability of winning the prize, in Tullock s model, is e, where e is the expenditure of e contestant i, N > 1 is the number of contestants and r 0 determines the impact of a change in expenditure on the probability of winning. In this model, in the case of perfectly discriminating (r = ), the contestant with the highest expenditure wins the contest with a probability of 100%, and this type of rent-seeking can be considered as an all-pay auction. Rent-seeking has been extensively studied, and the detailed review of studies on rent-seeking can be found in Congleton et al. (2008), Houser and Stratmann (2012), and Long (2013). Rent-seeking is perhaps the most similar game to some of the competition models in OM. For example, for r = 1, the Tullock s rent-seeking function is similar to the proportional demand allocation function which has been employed in studies like Benjaafar et al. (2007), Chen et al. (2012), Elahi (2013), Chen and Zhao (2015), and Elahi and Blake (2015). Following the behavioral research on simultaneous games in the economics literature, in recent years, a few researchers have started experimentally investigating the developed models in the simultaneous competitions in the OM literature to scrutinize behavioral biases in these setups. For instance, Chen et al. (2012) examine a competition between retailers for the limited capacity of a common supplier. They investigate the decisions of the retailers experimentally, and by comparing the results with theory find that the subjects average order is lower than what the Nash equilibrium predicts. To determine whether bounded rationality can lead subjects to make random errors in their decisions, they use the QRE model and find that players in a supply chain competition become more rational through repeated decisions, and that their decisions approach theoretical predictions as the experiment proceeds. In another experimental study, Chen and Zhao (2015) study a capacity allocation game with two identical retailers and one supplier who uses a proportional allocation scheme to allocate a limited capacity. The authors define a critical fractile factor to reflect the profit margin of each unit allocated to the retailers and aim to explain the observed behavior of the subjects by using it. As another example, Elahi and Blake (2015) study the competition of two suppliers for the demand of a single buyer. They find that in most cases, suppliers decisions are significantly different than the Nash equilibrium. The authors use an extended version of QRE method to quantify the impact of various factors on decisions of the players under different competition setups and find that loss aversion, rival chasing, and the gamesmanship behavior account for their experimental results. The game setup that Elahi and Blake (2015) have investigated, called multi-sourcing, is a common scenario in the real world because of its advantages. Multi-sourcing gives the companies the chance of hedging supply risks which companies deal with in a single sourcing approach, risks like disabled supply due to material shortages, machine breakdowns, and natural disasters (Minner 2003). Multi-sourcing, in the presence of the demand uncertainty, helps companies to improve the responsiveness to customers by guaranteeing the availability of products, especially Page 4 of 27

6 in today s global supply chains. Moreover, findings of prior studies show that the implementation of multi-sourcing can reduce inventory holding and shortage costs. Multi-sourcing has been studied in many studies in the literature, and a detailed review can be found in Minner (2003), and Yao and Minner (2017). The enormous amount of research in this area argues the importance of the multi-sourcing in OM literature, which in turn shows the importance of decision-making in it. Hence, the behavioral study of multi-sourcing can help researchers to explore suppliers decision-making process, and adjust their models based on their observations. Practitioners also can benefit from findings of these studies in making better decisions. Therefore, in this review study, we focus on the supply chain setup presented in Elahi (2013) to discuss each behavioral factor and propose the future research avenues. This setup consists of a single buyer who outsources the production of a product among N potential make-to-stock suppliers. Demand from the buyer is generated according to a Poisson process and is allocated proportionally to suppliers based on the competition criteria. We employ this setup as an example to more clearly explain each behavioral factor, and discuss effects of these factors on the individuals decisions in more detail. However, our findings can be extended to other simultaneous competitions in OM literature as well. 3. Behavioral Factors in Literature Prior experimental studies in both economics and OM have shown that individuals deviate from theoretical predictions. A large amount of research has been done to model individuals' behavior and explain the observed deviations. A prevalent stream of research in this area is considering some behavioral factors and cognitive biases which affect decision-making process and people's decisions. Systematic individual decision biases, or deviations from theoretical results is the key parameter in the extension of neoclassical behavior (Camerer 1999). Tversky and Kahneman (1975) in their seminal paper described three main heuristics, namely availability, representativeness and the anchoring-and-adjustment heuristic, that people use in their judgments. They also explain that these heuristics are useful in making a decision and arriving at a judgment, although they can lead to systematic errors that are defined as cognitive biases. Over the past decades, behavioral factors have been investigated in decision-making studies, especially in economics. Experimental studies of rent-seeking games and auction theories are two major streams of this type of research. In recent years, this type of research has found its way into OM literature, however, there are few articles in this area. For instance, Schweitzer and Cachon (2000) were the first to demonstrate a systematic deviation from optimal orders in newsvendor problem. This section identifies some behavioral factors investigated in both economics and OM literature, and briefly explains the relevant studies and their findings. Moreover, we find some gaps in prior researches and recommend some research topics as future work in BOM Anchoring and Adjustment Kahneman and Tversky (1975) identified three heuristics commonly used in probability judgments, and anchoring and adjustment is one of them. Anchoring is one of the most important decision biases which occurs when the estimation of a numerical value is based on an initial value (anchor), which is then insufficiently adjusted to provide the final answer (Tversky and Page 5 of 27

7 Kahneman 1975). This heuristic is a well-studied bias in different contexts, and in OM, newsvendor problem is one of these contexts. In newsvendor problem, a decision-maker orders inventory before a selling season to meet its stochastic demand, and experimental studies show that newsvendors make some systematic errors when they want to order. Many of studies in this context have investigated anchoring and adjustment heuristic as a possible explanation for observed ordering behavior of their subjects (e.g. Schweitzer and Cachon 2000, Benzion et al. 2008, Bolton and Katok 2008, Bostian et al. 2008, Kremer et al. 2010, Rudi and Drake 2014) and have found that the anchoring and adjustment heuristic, in most cases, account for participants ordering decisions and causes the systematic biases. Despite many studies in this area, still it is not clear how anchoring affects individuals decisions, and, as findings of prior studies show, decisions can be influenced differently in different situations. For example, anchoring on mean demand is one way that decisions are affected, and this phenomenon has been studied as pull-to-center effect in the literature. The pull-to-center effect, indeed, is the tendency of average order quantities to the mean demand of the game. Schweitzer and Cachon (2000) is the first experimental study of newsvendor problem in which the authors found that the average order quantities of the participants are too high when they should be low and are too low when they should be high (pull-to-center effect). Another effect of anchoring is demand-chasing which is defined as adjusting order quantities towards prior demand (Schweitzer and Cachon, 2000). Indeed, in a repetitive game with a probabilistic demand, subjects pay more attention to the demands of prior rounds, and this affects subjects' order decisions to be in correlation with past demands. Schweitzer and Cachon (2000) investigate this phenomenon and in their concluding discussion identify demand-chasing heuristic as one of the most promises for explaining their results. Effects of this bias have been investigated in some other laboratory experiments of newsvendor game as well, and their results show that demandchasing can account for the observed behaviors (e.g. Bostian et al. 2008, Benzion et al. 2008, Kremer et al. 2010, Rudi and Drake 2014). Anchoring and adjustment heuristic has been studied in some other contexts as well. For example, Rapoport (1967) investigates a multi-stage inventory ordering task and finds that ordering decisions, contrary to normative models, are strongly correlated with past demand. Sterman (1989a) finds that anchoring and adjustment heuristic accounts for observed ordering behavior in the beer distribution game. In a study of the performance of supply chain contract mechanisms, Katok and Wu (2009) investigate the performance of the wholesale price contract, the buyback contract, and the revenue-sharing contract and compare the three mechanisms in a laboratory setting. The authors find that anchoring and adjustment appear to be a reasonably accurate description of behavior under the wholesale price contract, although it cannot account for the observed behavior under coordinating contracts. Moreover, the results show that demandchasing behavior significantly exists in each of the retailer game treatments, however, is not significant in any of the supplier game treatments. Apart from that, the presented information to the subjects have a key role in anchoring and adjustment heuristic, especially, in a repetitive game where subjects get informed about the results of the prior rounds (e.g. demand, decisions of other players, pay-offs of the chosen decision). The question here is how subjects decisions are affected by the time and content of shared information. This question can be explained by availability heuristic (Tversky and Page 6 of 27

8 Kahneman, 1973). Tversky and Kahneman (1973, p. 207) define the availability heuristic as a judgmental heuristic in which a person evaluates the frequency of classes or the probability of events by availability, i.e., by the ease with which relevant instances come to mind. Under this heuristic, people tend to heavily weigh their judgments toward more recent information, or the information that comes easier to their mind when evaluating a specific decision. In most of the experimental competition studies, subjects participate in a repetitive game and make numerous decisions in some sequential rounds. In this case, it is more probable that the subjects make their decisions in each round biased toward the results and information which come to their mind easier and faster (anchor). Some studies show that both frequency of feedback and the information that is presented to the subjects can affect their decisions. For instance, in a field study, Zeelenberg and Pieters (2004) find that level of anticipated post-decisional regret is influenced by particular feedback which is present in the Postcode Lottery, but absent in the State Lottery, and feedback moderates the influence of anticipated regret on lottery participation. As another example, Engelbrecht-Wiggans and Katok (2008), in a study of the effect of regret-related feedback information on bidding behavior in the sealed-bid first-price auctions, analyze four information conditions where subjects were provided with a very different amount of feedback information. The authors find that participants learn faster in conditions with better feedback, and this fact better explains their results. Effects of feedback and information have been investigated in some studies of newsvendor game which show that these factors influence order quantities (e.g. Bolton and Katok 2008, Rudi and Drake 2014). Recommendations for Future Work As is discussed, especially in the findings of Katok and Wu (2009), effect of anchoring and adjustment heuristic could be different in different games and also for different parties of a game. Hence, researchers should be careful about differences that exist between different games, and they have to redesign the experiments carefully when they want to bring a phenomenon to a new context. Sometimes some phenomena and the way they affect decisions could be different in new settings. For example, a simultaneous game is different from newsvendor game. Therefore, anchoring and adjustment heuristic might affect individuals behavior differently, or some other types of anchors could exist. For instance, Elahi and Blake (2015) state that other explanations for anchoring might be considered in the simultaneous games. The authors, in their experimental study of the supplier competition, find that subjects in each round adjust their decisions toward their rival s decision in the prior rounds. Elahi and Blake (2015) explain this observation as rivalchasing, and show that this phenomenon significantly explains the observed behaviors in some of their experimental treatments. Findings of this study raise this question that how subjects behave in presence of both rival-chasing and demand-chasing behavior, which especially exists in simultaneous competitions. In such a game, subjects behavior is more affected by the demand in the prior rounds or the revealed decision of the rivals? In literature, the general form of the proposed model to investigate the anchoring and chasing behavior is: q = αa + (1 α)q + ε 0 α 1 In this equation, q is the decision in round t, q is the optimal or normative decision of the game, A is the anchor, α is the weight that subject give to the anchor (i.e., tendency to the anchor), and ε is the error term. Here, A can be the demand distribution mean (Schweitzer and Cachon Page 7 of 27

9 2000, Benzion et al. 2008, Bostian et al. 2008, Kremer et al. 2010), demand in the most recent round (Schweitzer and Cachon 2000, Bostian et al. 2008, Kremer et al. 2010), rival s decision (Elahi and Blake 2015) and any other factor that might anchor subjects decisions. In more general form, we can think about effect of multiple anchors at the same time and formulate the decision as follows: q = α β A + (1 α )q + ε where β Here, n is number of the anchors affecting subjects decisions in a study, β is the weight that subject gives to the anchor A, α is weight of all anchors, and other parameters are same as before. Moreover, we assumed that subjects anchor points, and their weights vary through the rounds. Consequently, doing so helps us to examine effects of different anchors at the same time. In a supplier competition, as an example, we can investigate effects of both demand and rival chasing to know how people select the provided information and weigh on different parts of it. Besides that, as we discussed, feedback frequency and shared information are important factors in behavioral studies, and they affect individuals decisions. Moreover, feedback and shared information not only affect individuals decisions but also are important parameters in designing an experiment. A precise experimental design is a crucial part of each behavioral study to correctly measure what is desired. Moreover, employing feedback and information as two research design parameters allows researchers to have more various settings leading to study individuals behaviors more accurately. For instance, Engelbrecht-Wiggans and Katok (2009) design an experiment in which by varying the amount of feedback and the payment rule in addition to varying the type of feedback, separate the effects of regret from risk aversion. Additionally, exploring influences of feedback on adjusting behavior of the subjects is an interesting research topic. Lawrence et al. (2006, p. 507) by reviewing over 200 studies in judgmental forecasting find that feedback can be valuable because it enables the judgmental forecaster to learn. In repetitive games, providing feedback to the subjects to be informed on the payoff of their decisions can help them to learn and choose better decisions in the proceeding rounds. However, the improvement depends on how the subjects interpret the provided information, and which part of information has more influence on them. To the best of our knowledge, there is no study of effects of feedback frequency and shared information in the context of simultaneous games in OM literature. Therefore, future research in this area can investigate these effects and enrich the behavioral research literature. For example, by controlling the feedback frequency and the shared information in a supplier game, we can investigate how suppliers adjust their decisions, and which information has the most influence on their decisions. This approach also can be used to design some experiments to answer the questions about chasing behavior of the suppliers. In addition to theoretical contributions, findings of research in this area have some practical implications as well. In a real-world game, for example, a manager who wants to buy a product from different suppliers, can control the feedback and the shared information between the players to gain more payoffs. Apart from the feedback frequency, the frequency of decisions is another factor that might affect subjects decisions in an experiment. Bolton and Katok (2008) considered an experiment condition in which subjects were restricted to order a fixed quantity that would be applied to the next 10 demand rounds. They found that when decisions are made every 10 rounds instead of every round, the performance of the decision-makers is enhanced and negative correlations = 1 Page 8 of 27

10 between rounds and anchoring on mean demand are reduced. These results suggest that making decisions too frequently can result in adverse consequences. The frequency of decisions is not studied well in literature, so it can be studied in various games, and also in different experimental conditions. Investigation of decision frequency and its effects on decisions, besides helping managers in improving their performance by controlling the decision periods, can help researchers in better understanding how people make their decisions, so they can explain individuals behaviors more accurately. Understanding how demand-chasing, rival-chasing, anchoring and adjustment behavior might be influenced by the frequency of decisions could be a valuable research area in BOM Prospect Theory and Framing Expected utility theory is one of the first theories explaining rational decision-making under uncertain outcomes. This theory assumes that people choose the outcome which results in the highest expected utility, and plays a leading role in the standard economic analysis. This theory is based on some assumptions about human behavior. However, experimental studies on decisionmaking under uncertainty have shown that people often violate the expected utility theory axioms when making their decisions. Indeed, expected utility theory makes faulty predictions about people's decisions in many real-life choice situations (see Kahneman & Tversky 1982). Therefore, the explanatory power of expected utility theory is limited. Prospect theory (Kahneman and Tversky 1979) is a behavioral economics theory which tries to model real-life choices, rather than optimal decisions, and describes decision-making more accurately, compared to the expected utility theory. This theory proposes that preferences are defined by the deviation from a reference point rather than by the final state of the outcome, and positive deviations are the gains and negative deviations are losses (Kahneman and Tversky 1979). Moreover, prospect theory argues that people s decisions rely on their decision weights rather than probabilities when evaluating risky choices. These decision weights transform the probability of outcomes in a nonlinear manner, i.e., overweighting small probabilities and underweighting medium probabilities. Indeed, this theory implies that people are not risk-neutral, and they show risk-averse behavior when facing moderate probabilities of gain or small probabilities of loss, however, they are riskseeker when gains have small probabilities or losses have moderate probabilities. In literature, decision-makers in many models are assumed to be risk-neutral and loss neutral. However, there are many experimental studies showing these assumptions are violated in a real decision-making process (e.g. Milner and Pratt 1991, Goeree et al. 2002, Ho and Zhang 2008, Ho et al. 2010). Although some experimental studies could not explain their empirical findings by prospect theory (e.g. Schweitzer and Cachon 2000, Nagarajan and Shechter 2013), there are many researches employing prospect theory in their models which can better explain the observed behaviors (e.g. Wang and Webster 2009, Long and Nasiry 2015). Prospect theory shows that a loss is more significant than the equivalent gain, a sure gain is favored over a probabilistic gain, and a probabilistic loss is preferred to a definite loss. Hence, how a situation is described influences people s way of thinking, in particular, the mental representations, interpretations, and simplifications of reality. Indeed, how a situation is framed can affect people s behavior, so it can change the outcome of the choice problems (Tversky and Kahneman 1985). Therefore, framing is an important parameter in designing and conducting experimental studies and ignoring it can lead to wrong results, so researchers should take great care about framing and its effects on the Page 9 of 27

11 participants behavior in their studies (Katok 2011). In a literature review of framing, Levin et al. (1998) divide 93 studies into three types of framing and find that effects of risky choice framing, the most consistent type, reveals a relatively consistent tendency for people to be more likely to take risks when options focus attention on the chance to avoid losses than when options focus on the chance to realize gains (Levin et al. 1998, p. 153). Schultz et al. (2007) experimentally investigate this finding in an inventory decision study, and their results do not support it. However, some researches in BOM have investigated effects of framing on subjects decisions and have found that it matters. For example, Ho and Zhang (2008), in their study of the role of framing in channel efficiency, compare a two-part tariff with an all-unit quantity discount. The authors find that the fixed fee fails to increase the efficiency of the channel when framed as a two-part tariff, but achieves a higher efficiency when framed as a quantity discount, that is contrary to the theory which predicts an equal efficiency for these two mechanisms. In another laboratory setting, Katok and Wu (2009) compare the performance of the wholesale price contract, the buyback contract, and the revenue-sharing contract mechanism and study impacts of framing on subjects decisions through loss aversion. The authors observe some differences between the two coordinating contracts, which are supposed to be the same, and conclude that framing is the only possible explanation. These studies show that framing effect not only might result in different perceptions of the same game but also can influence different games with the same theoretical results to have different results in practice. Recommendations for Future Work Future research in BOM can be done to investigate Levin et al. s finding, which is also implied by prospect theory, in more detail. Indeed, conducting some experiments to study how results of the same game might be different when it is framed in diverse ways. Moreover, some experiments can also be conducted to investigate how the combination of these two different effects of framing, on results of the same game and on results of different games, take place. For instance, in Elahi s supplier competition setup, nine different treatments exist, that suppliers decisions and performances are different in each of them. Future research can explore how framing each of these treatments in a different way or like another treatment, can influence subjects behavior, and does their decisions be adjusted toward the framed treatment ones. In addition, it seems that framing s influence on behavior can be stronger in initial rounds of a repetitive game, and it might be disappeared with experience. Further research can be done to study how framing s effect changes with experience, and can learning diminish this effect. Recently, findings of some studies reveal that assuming a status quo, i.e. zero payoff, reference point in prior studies have caused that prospect theory could not explain the ordering behaviors, however, there are situations in which gains and losses are coded relative to an expectation or aspiration level that differs from the status quo (Kahneman and Tversky 1979, p. 286). Hence, they propose an alternative reference point, which can better explain the observed ordering behaviors (Long and Nasiry 2015, Uppari and Hasija 2017). Moreover, these studies show that the reference point can be different in different treatments and for different subjects. Hence, further research can investigate how the reference point might change in different games and in different treatments. Besides this effect, what is the effect of framing on the reference point? Indeed, how the reference point would be affected by the way that a problem is framed? As Tversky and Kahneman (1985) argue, the way that a situation is described, or a problem is explained affect Page 10 of 27

12 people s attitude toward gain and loss and might change their perception of them. Therefore, it can be inferred that framing influences the reference point of subjects. Furthermore, as is explained in Long and Nasiry (2015) and Uppari and Hasija (2017), reference point could depend on the realized demand and the order quantity, indeed, it is a payoff function of them. And, as is shown in the literature, in repetitive games, where information of the round, such as demand, is provided to the subjects, they pay more attention to some parts of the provided information and make their decisions in the proceeding round based on them (anchor). Altogether, it can be inferred that the reference point might be influenced by the revealed data. In other words, subjects change their reference point over the rounds in a game, and we are faced with dynamic reference point. This phenomenon can be more important in a simultaneous game, where the subjects get informed about their rivals decisions and payoffs too. For example, in a supplier competition, when a subject understands that his rival s payoff in the preceding round was more than what he has gained, this greater payoff might be a new reference point. What about the reverse case? Does a lower profit of the rival make the player less ambitious and make their gain area larger? Developing some novel models to study the dynamic reference point, and validating them by real world observations helps to answer these questions Misperception of Probabilities As we explained in the prior section, the explanatory power of the expected utility theory is limited, and it cannot be used to predict some real-life decisions. Hence, several attempts were made to model probabilistic decision-making problems. One of these attempts, as we explained, is prospect theory introduced by Kahneman and Tversky (1979). However, this model involved violations of first-order stochastic dominance. Tversky and Kahneman (1992) to answer this problem developed their model by applying weighting to the cumulative probability distribution function and introduced cumulative prospect theory. Another attempt to develop a more generalizable model is nonlinear probability weighting that is one of the strongest ones, and in particular, the rank-dependent version of nonlinear probability weighting. In this model, we can replace the original probabilities over outcomes by transformed ones, and recalculate expected payoffs. The idea here is that people may maximize expected utility, but misperceive probabilities, and make their decisions based on these misperceived probabilities. In the literature of behavioral economics, Milner and Pratt (1989) support this effect and state that the amount of rent that is dissipated in a rent-seeking game is affected by the manner in which the probability of receiving a rent is determined. Goeree et al. (2002) in their study of a first-price private values auction and Parco et al. (2005) in their study of a rent-seeking game use a probability weighting function and show that the predictive accuracy of these descriptive models is better than that of the normative ones. Probability assessment and forecasting is a well-studied topic in some other research areas. For example, Lawrence et al. (2006) review the published papers during 25 years in judgmental forecasting literature and find that overconfidence, poor calibration, desirability, imminence, time period, and perceived controllability of events may affect probability assessments and their calibration. Furthermore, optimistic bias (Weinstein, 1980) might positively be correlated with people s perception of controllability of events (Lawrence et al. 2006), and the combination of overconfidence and optimism is a potent brew, which causes people to overestimate their knowledge, underestimate risks, and exaggerate their ability to control events (Kahneman & Riepe, 1998, p. 54). Lawrence et al. (2006) explain these heuristics and biases in judgmental Page 11 of 27

13 probabilistic forecasting context and discuss main strategies for improving judgmental forecast, including provision of feedback, decomposition, combining and correction. Recommendations for Future Work Almost all the studied games in BOM literature consist of two different decision parts: forecasting and ordering. For example, in a multi-sourcing competition, decision-makers (suppliers) should first forecast other suppliers decisions, and then make their decisions based on their forecasts and the allocation rules. One of the main strategies to mitigate heuristics and biases in this case is decomposition. Decomposition methods are designed to improve accuracy by splitting the judgmental task into a series of smaller and cognitively less demanding tasks, and then combining the resulting judgements (Lawrence et al. 2006, p. 507). Schweitzer and Cachon (2000) propose separation of the forecasting and inventory decision task as an approach to improve inventory order decisions. Kremer et al. (2011) use a controlled laboratory experiment to analyze how individuals make forecasts based on time-series data, and they find that forecasting behavior systematically deviates from normative predictions. The authors suggest that demandchasing in newsvendor problem is not exclusively related to inventory ordering and might be a forecasting phenomenon in which the perceived probability has a great role. How people behave in each of forecasting and ordering phases? Which biases are more present in each of these phases, and how they play a role? Does a bias influence the subjects in a same way in both forecasting and ordering steps? Further, in the simultaneous games, perceived probability and forecasting can have a stronger effect. In the supplier competition, for example, forecasting is more important, because the players not only have to forecast the buyer s demand but also should predict their rival s order quantity. Therefore, decomposing such experimental decisions into their forecasting and ordering components would be a worthwhile research that allows researchers to explore decision-making process in more detail. Findings of prior studies show that overconfidence is an important bias in probability assessment (Lawrence et al and references therein; Montibeller and Winterfeldt 2015). Prior research implies that individuals display overconfidence in a wide range of applications (see Muller (2007) for an extensive review). Some current researches have studied the impact of overconfidence in the newsvendor model (e.g., Croson et al. 2008; Ren and Croson 2013) and have found support for it. Understanding how overconfidence influence people s perceptions, data selection approach, weighing provided information, and analyzing them benefits both researchers and practitioners. This aim helps researchers to develop better decision models predicting people s behavior more accurately. Moreover, these models can be put into decision support systems to help managers in mitigating effects of overconfidence. Managers also can benefit from knowing more about overconfidence and its effects to be away from unpleasant outcomes of the overconfident decision-making Emotions and Feelings When people come to play, it must be considered that people not only are heterogeneous decision-makers but also have different emotions and feelings when making their decisions. In the process of thinking, two types of cognitive processes are distinguished: (1) system 1, and (2) system 2 (Stanovich and West 2000). Although the operations of System 2 are deliberately controlled and potentially rule-governed, the operations of System 1 are automatic, effortless, Page 12 of 27

14 governed by habit, and often emotionally charged (Kahneman 2003). When people are making a fast decision, system 1 prevails system 2 in most cases, so their decisions would be affected by their emotions. Therefore, emotion is part of utility, and it should be considered in developing choice theories, as Kahneman (2003, p. 1457) states that a theory of choice that completely ignores feelings such as the pain of losses and the regret of mistakes is not only descriptively unrealistic, it also leads to prescriptions that do not maximize the utility of outcomes as they are actually experienced. Moreover, some non-pecuniary factors are usually part of utility which should be considered in modeling and maximizing people's utilities. Rottenstreich and Hsee (2001) show that when people are valuing chances to receive emotionally loaded outcomes are less sensitive to variations of probability than when the outcomes are monetary. Here we discuss three emotional attributes which can be included in individual s utility function: regret, joy-ofwinning, and fairness Regret Theory and Joy-of-Winning Regret theory is another theory developed as an alternative to expected utility theory. Regret was first introduced by Savage (1951), and then Luce and Raiffa (1958), Bell (1982), and Loomes and Sugden (1982) further explore it. After making a decision, people compare the consequences of the particular choice with those of another choice that they could have made and depending on the outcome of this comparison, experience regret or rejoicing. This experience affects their following decisions, and they anticipate the possibility of a regret or rejoicing experience when they actually want to make a decision. Researchers have used this theory in their studies to develop new theoretical models and explain the observed behavior of individuals. For instance, Inman et al. (1997) develop a model of post-choice valuation which is based on the sum of three components representing factors that may contribute to consumers' assessment of a chosen product or service: (1) expected performance, (2) disappointment, which captures the discrepancy between actual and expected performance, and (3) regret, which captures the difference between the performance of the chosen product/service and the performance of a foregone one. The authors find that post-choice valuation can significantly be affected by performance information about "forgone" alternatives. In auction theory, Morgan et al. (2003) develop a theoretical model of "spiteful bidding" in which " a bidder cares not only about her own surplus in the event she wins the auction but also about the surplus of her rivals in the event she loses " (Morgan et al. 2003, p. 1). In another study, Engelbrecht-Wiggans (1989) looks at regret specifically in the context of first-price auctions and investigate two types of regret: (1) Winning and paying too much, which states winner of the auction may regret paying too much relative to the second highest bid; and (2) Missing an opportunity to win at a favorable price, which is regret of a loser because of missing an opportunity to win at a favorable price. The author proposes a model which suggests, under very general conditions, being sensitive to winning and paying too much should result in lower average bids, and being sensitive to missing opportunities to win at a favorable price should result in higher bids. Engelbrecht-Wiggans and Katok (2007, 2008 & 2009) extend this model and experimentally investigate the impact of these two types of regret on the bidding behavior in sealed-bid first-price auctions. The experimental results show a strong support for both of the predicted behaviors, and these treatment effects persist over time. The authors find that subjects put more weight on the loser s regret (missing an opportunity to win at a favorable price) than on the winner s regret (winning and paying too much). The findings of this study are in line with the behavioral studies which propose joy-of-winning as one emotional factor of Page 13 of 27

15 individual s utility function. Psychological research shows that men do not work to maximize their economic benefits, any more than they try to maximize their physical comfort. What does a billionaire need a second billion for? To be of higher rank than a fellow billionaire who only has a single billion (Barkow 1989, p. 196). This statement shows that sometimes individuals are interested in being the winner of a competition and enjoy their winning. Schmitt et al. (2004) confirm this opinion and propose that winning may be a component in a subject s utility. Some other researchers have considered joy-of-winning as a factor in people s utility function as well, and have studied it to explain the observed behavior of individuals. For instance, in auction literature, some researchers have investigated this phenomenon and find that a model in which players experience a "joy-of-winning" provides a reasonable fit to the data and account for bidding behavior (e.g. Cox et al. 1992, Holt and Sherman 2000, Goeree et al. 2002). In another study of auctions, Goeree and Offerman (2003) conduct a series of experiments and find that the joy-ofwinning model fits the experimental data almost good, but the model predicts a negative joy-ofwinning and is therefore rejected. However, it seems that this negative effect might be explained by winner s regret (winning and paying too much) in which people worry about paying too much, so in this case, they show a behavior in contrast with joy-of-winning. Joy-of-winning has been experimentally studied in rent-seeking literature as well, and the results show that winning is a component in subject's utility (e.g. Parco et al. 2005, Sheremeta 2010). Additionally, in a field study, Zeelenberg and Pieters (2004) investigate regret and its influence on decision-making in real-life lotteries, and find that the level of anticipated post-decisional regret is influenced by particular feedback which is present in the Postcode Lottery, but absent in the State Lottery, and feedback moderates the influence of anticipated regret on lottery participation. A few studies in OM literature have experimentally investigated regret and joy-of-winning and the way they affect subjects decisions in a game. Perakis and Roels (2008) theoretically study the newsvendor problem and derive the order quantities that minimize the newsvendor's maximum regret of not acting optimally. Schweitzer and Cachon (2000) in their seminal study of the newsvendor problem, apply regret theory to their model by considering the newsvendor s preference as minimizing ex-post inventory error, the deviation between the order quantity and the realized demand and find experimental evidence that this effect occurs. Katok and Wu (2009), in their study of the performance of supply chain contract mechanisms, find the desire to minimize ex-post inventory error as well, and they explain this behavior as the regret from having a mismatch between the order and the demand. In a study of simultaneous competition of suppliers for the demand of a single buyer, Elahi and Blake (2015), to explain the observed deviation of subjects decisions from theory, examine the impact of three behavioral factors: (1) loss aversion, (2) rival chasing, and (3) the gamesmanship behavior. The latter factor in this study is defined as the contestants tendency to beat the competition instead of maximizing the profit, which is a similar factor to joy-of-winning in other behavioral studies. However, in this study, the authors propose an equilibrium model to investigate this behavior Fairness and Inequality Aversion As is explained, there are some non-pecuniary factors in people s utility functions, and economic benefits are not the only factor of utility. One of the prominent non-monetary motivations of people is the desire to be treated fairly and in some cases the desire to treat others fairly (Katok and Pavlov 2013). Fairness have been studied in the behavioral economics literature, Page 14 of 27