Inductive Cognitive Models and the Coevolution of Signaling

Transcription

1 of of Analytis Max Planck Institute for Human Development October 18, 2012

2 of Appendix

3 of It simply was not true that a world with almost perfect information was very similar to one in which re was perfect information. -Joseph Stiglitz

4 of ory has had an increasing impact in Economics, Biology and or Social Sciences.

5 of Experimental and oretical investigations have demonstrated a number of oretical limitations.

6 of Addressing many of limitations within Bayesian game oretic framework is impossible.

7 of In many signaling situations agents think inductively rar than deductively. Employing inductive models and agent based simulations we can expand scope of signaling ory and integrate signaling models with inductive psychology.

8 of It simply was not true that a world with almost perfect information was very similar to one in which re was perfect information. -Joseph Stiglitz ory has had an increasing impact in Economics, Biology and or Social Sciences. Experimental and oretical investigations have demonstrated a number of oretical limitations. Addressing many of limitations within Bayesian game oretic framework is impossible. In many signaling situations agents think inductively rar than deductively. Employing inductive models and agent based simulations we can expand scope of signaling ory and integrate signaling models with inductive psychology.

9 The Basic Model of

10 Furr Developments and Limitations of The domain of application of signaling ory has expanded to limit pricing, finance, advertising, biology, politics and taxi driving. Noise, multiple agents and multiple signals have been introduced in basic model one at a time. models have multiple equilibria. Equilibrium selection has been a persistent issue for orists. John Riley (2001), Silver Signals, JOEL While underlying ory may seem well settled, much work remains. I have emphasized need for furr discussion of equilibrium in which screening/signaling costs are not perfectly correlated with quality.

11 Theory : Experiments of Experiments are characterized by suggestive dynamics. The results illustrate that separation of types is rarely perfect. Simple learning models can account for results better than equilibrium refinements such as divinity and Intuitive criterion. Experimental Literature 1 Miller and Plott (1985). 2 Cooper and Kagel (1994,1997a,1997b,2003,2005, 2008). 3 Brandts and Holt (1992,1993); Banks, Camerer and Porter (1994). 4 Cadsby et al (1990,1998); Potters and Van Winden (1996); Kubler et al (2008); Guth and Winter(2012). 5 De Haan et al (2009) ; Jeitschko et al (2009).

12 Do signaling orists need to talk to psychologist(s) of

13 of 1 A great deal of psychology is studying how people access and integrate information. 2 There are plenty of inductive models, some of m very recent, inspired from statistics and machine learning. 3 They make clear-cut predictions and can be tested against each or. 4 Could we implement induction in signaling models?

14 From Bayesian Equilibria to Inference of Evolutionarily Stable State, Grafen (1990) (1) w[a (q), P (A (q)), q] w[a, P (a), q] for all a,q. (2) D[q, P (A (q))]dg(q) D[q, P (A (q))]dg(q) for all functions P(a). w(a, p, q) = male s fitness, D(q, p) = loss of fitness due to incorrect assessment, A(q) = Advertising, P (a) = Perceived value of a male,q = male quality. From deduction to induction Step 1 : Introduce inductive models. Step 2 : No perfect negative correlation. Step 3 : Studying coevolution.

15 The Model : Basics and Parameters of Sending agents and receiving agents. There is a negative correlation r between quality of sending agents qɛq = {1, } and ir cost of advertising cɛc = {1, }. q can not be directly observed by receivers. The senders inherit an advertizing strategy aɛa = {1, }. Receivers encounter a group of senders picked randomly from population with replacement. Receivers have a monotonic pay-off function d(q) = q. They can select using a regression an exemplar model or a heuristic. The senders receive a reward r every time y are selected. The cost of signaling is s q 1.25

16 Inference Strategies of Receivers are ecquiped with a memory where y can store ir experiences. The receivers store quality and amount of advertizing of senders y select in ir memory Inference Strategies Fisher s rule : Always choose agent with highest signal. Regression : Use data in memory to build a linear model. Exemplar : Infer quality from most similar signal seen in past.

17 of For senders evolution is taking place for each level ofq. 3 agents are picked at random from population. The agent with highest accumulated reward r is reproduced and an agent is eliminated at random. The process is repeated 10 times for each quality level. There is a mutation level m = Receivers : The receivers reconsider ir strategy with probability p = The receivers choose strategy that is most accurate at that point of time.

18 Strategy Accuracy of correlation = 0.82, noise = 3, group = 10, memory = 30 % Correct Inferences Fisher' rule Exemplar Regression Strategy Performance Round

19 Strategy Accuracy of correlation = 0.82, noise = 0,1, group = 10, memory = 10 % Correct Inferences Fisher' rule Exemplar Regression Strategy Performance Round

20 The Emergence of of correlation = 0.82, noise = 3, group = 10, memory = 30 Strategies Average signal cost=1 cost=3 cost=5 cost=7 cost=

21 of behavior can emerge even when n correlation between quality and cost is not perfectly negative.

22 of A simple hard wired preference beats in many scenarios memory based strategies in terms of performance.

23 of As size of sample grows performance of memory based strategies improves. However exemplar model is prone to noise and regression prone to a selection bias.

24 of The most exciting developments in signaling games in future are likely to come from interaction between economics and or disciplines.-joel Sobel (2008); Games. Encyclopedia of Complexity and Systems Science

25 of behavior can emerge even when n correlation between quality and cost is not perfectly negative. A simple hard wired preference beats in many scenarios memory based strategies in terms of performance. As size of sample grows performance of memory based strategies improves. However exemplar model is prone to noise and regression prone to a selection bias. The most exciting developments in signaling games in future are likely to come from interaction between economics and or disciplines.-joel Sobel (2008); Games. Encyclopedia of Complexity and Systems Science

26 Unanswered questions of Model environments with more than possible signals and study interactions among m. Examine when and why new signals are likely to arise in a society. Use non-static environments to examine robustness of different inference algorithms. Adapt model to economics and explore possible applications.

27 Population Dynamics of correlation = 0.82, noise = 3, group = 10, memory = 10 Population Dynamics # of Strategies Fisher's rule Exemplar Regression

28 Strategy Accuracy of correlation = 0.82, noise = 3, group = 10, memory = 30 % Correct Inferences Fisher' rule Exemplar Regression Strategy Performance Round