We demonstrate that a simple model, constructed on the premise that people are motivated by both their pecuniary payoff and their relative payoff standing, organizes a large and seemingly disparate set of laboratory observations as one consistent pattern The model is incomplete information but nevertheless posed entirely in terms of directly observable variables The model explains observations from games where equity is thought to be a factor, such as ultimatum and dictator, games where reciprocity is thought to play a role, such as the prisoner's dilemma and gift exchange, and games where competitive behavior is observed, such as Bertrand markets (JEL C78, C90, D63, D64, H41)

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ERC: A Theory of Equity, Reciprocity, and Competition

In 1974 an article appeared in Science magazine with the dry-sounding title “Judgment Under Uncertainty: Heuristics and Biases” by a pair of psychologists who were not well known outside their discipline of decision theory. In it Amos Tversky and Daniel Kahneman introduced the world to Prospect Theory, which mapped out how humans actually behave when faced with decisions about gains and losses, in contrast to how economists assumed that people behave. Prospect Theory turned Economics on its head by demonstrating through a series of ingenious experiments that people are much more concerned with losses than they are with gains, and that framing a choice from one perspective or the other will result in decisions that are exactly the opposite of each other, even if the outcomes are monetarily the same. Prospect Theory led cognitive psychology in a new direction that began to uncover other human biases in thinking that are probably not learned but are part of our brain’s wiring.

Thinking fast and slow.

The author systematically examines one of the important issues of information — establishing the market price. He introduces the concept of «search» — where a buyer wanting to get a better price, is forced to question sellers. The article deals with various aspects of finding the necessary information.

Economics of Information

Handbook of Experimental Economics

Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

博弈论 : 矛盾冲突分析 = Game theory : analysis of conflict

Consider the following game: a large number of players have to state simultaneously a number in the closed interval [0, 100]. The winner is the person whose chosen number is closest to the mean of all chosen numbers multiplied by a parameter p, where p is a predetermined positive parameter of the game; p is common knowledge. The payoff to the winner is a fixed amount, which is independent of the stated number and p. If there is a tie, the prize is divided equally among the winners. The other players whose chosen numbers are further away receive nothing.' The game is played for four rounds by the same group of players. After each round, all chosen numbers, the mean, p times the mean, the winning numbers, and the payoffs are presented to the subjects. For 0 c p < 1, there exists only one Nash equilibrium: all players announce zero. Also for the repeated supergame, all Nash equilibria induce the same announcements and payoffs as in the one-shot game. Thus, game theory predicts an unambiguous outcome. The structure of the game is favorable for investigating whether and how a player's mental process incorporates the behavior of the other players in conscious reasoning. An explanation proposed, for out-of-equilibrium behavior involves subjects engaging in a finite depth of reasoning on players' beliefs about one another. In the simplest case, a player selects a strategy at random without forming beliefs or picks a number that is salient to him (zero-order belief). A somewhat more sophisticated player forms first-order beliefs on the behavior of the other players. He thinks that others select a number at random, and he chooses his best response to this belief. Or he forms second-order beliefs on the first-order beliefs of the others and maybe nth order beliefs about the (n I )th order beliefs of the others, but only up to a finite n, called the ndepth of reasoning. The idea that players employ finite depths of reasoning has been studied by various theorists (see e.g., Kenneth Binmore, 1987, 1988; Reinhard Selten, 1991; Robert Aumann, 1992; Michael Bacharach, 1992; Cristina Bicchieri, 1993; Dale 0. Stahl, 1993). There is also the famous discussion of newspaper competitions by John M. Keynes (1936 p. 156) who describes the mental process of competitors confronted with picking the face that is closest to the mean preference of all competitors.2 Keynes's game, which he considered a Gedankenexperiment, has p = 1. However, with p = 1, one cannot distinguish between different steps of reasoning by actual subjects in an experiment. There are some experimental studies in which reasoning processes have been analyzed in ways similar to the analysis in this paper. Judith Mehta et al. (1994), who studied behavior in two-person coordination games, suggest that players coordinate by either applying depth of reasoning of order I or by picking a focal point (Thomas C. Schelling, 1964), which they call "Schelling salience." Stahl and Paul W. Wilson (1994) analyzed behavior in symmetric 3 x 3 games and concluded that subjects were using depths of reasoning of orders 1 or 2 or a Nash-equilibrium strategy. * Department of Economics, Universitat Pompeu Fabra, Balmes 132, Barcelona 08008, Spain. Financial support from Deutsche Forschungsgemeinschaft (DFG) through Sonderforschungsbereich 303 and a postdoctoral fellowship from the University of Pittsburgh are gratefully acknowledged. I thank Reinhard Selten, Dieter Balkenborg, Ken Binmore, John Duffy, Michael Mitzkewitz, Alvin Roth, Karim Sadrieh, Chris Starmer, and two anonymous referees for helpful discussions and comments. I learned about the guessing game in a game-theory class given by Roger Guesnerie, who used the game as a demonstration experiment. 'The game is mentioned, for example, by Herve Moulin (1986), as an example to explain rationalizability, and by Mario H. Simonsen (1988). 2 This metaphor is frequently mentioned in the macroeconomic literature (see e.g., Roman Frydman, 1982).

http://www.parisschoolofeconomics.eu/docs/guesnerie-roger/nagel95.pdf

Unraveling in Guessing Games: An Experimental Study

Consider the problem of a consumer in a modern supermarket. The typical store sells more than 40,000 items, and in many product categories it offers hundreds of options (for a recent review see Simona Botti and Sheena S. Iyengar 2006). The typical consumer is also time constrained and cannot afford to spend too much time making each selection. To solve this decision problem consumers need to per? form a dynamic search over the set of feasible items under conditions of extreme time pressure and choice overload. This gives rise to several basic questions which are studied in this paper: (i) What are the computational processes deployed by consumers during the search and decision processes, and to what extent are they compatible with standard economic search models? (ii) How do the processes, and their performance, change with the number of options? (iii) Do the computational processes exhibit systematic biases that can be exploited by sellers to manipulate their choices? We study these questions by setting up an experimental version of the consumer's supermarket problem. Hungry subjects are presented with sets of 4,9, or 16 familiar snack items (e.g., Snickers candy bars and Lay's chips) and are asked to make a choice within three seconds. Items are displayed using pictures of the actual pack? ages of items. Besides choices and reaction times, the entire process of visual search is recorded using eye tracking.

https://www.rnl.caltech.edu/publications/pdf/reutskaja2011.pdf

Search Dynamics in Consumer Choice under Time Pressure: An Eye-Tracking Study

We used functional MRI (fMRI) to investigate human mental processes in a competitive interactive setting--the "beauty contest" game. This game is well-suited for investigating whether and how a player's mental processing incorporates the thinking process of others in strategic reasoning. We apply a cognitive hierarchy model to classify subject's choices in the experimental game according to the degree of strategic reasoning so that we can identify the neural substrates of different levels of strategizing. According to this model, high-level reasoners expect the others to behave strategically, whereas low-level reasoners choose based on the expectation that others will choose randomly. The data show that high-level reasoning and a measure of strategic IQ (related to winning in the game) correlate with the neural activity in the medial prefrontal cortex, demonstrating its crucial role in successful mentalizing. This supports a cognitive hierarchy model of human brain and behavior.

/pdf/neural-correlates-of-depth-of-strategic-reasoning-in-medial-3id4wvyvti.pdf

Neural correlates of depth of strategic reasoning in medial prefrontal cortex

This paper is about experiments on two versions of ultimatum games with incomplete information, called the offer game and the demand game. We apply the strategy method, that is, each subject had to design a complete strategy in advance instead of reacting spontaneously to a situation which occurs in the game. Game theory predicts very similar outcomes for the offer and the demand games. Our experiments, however, show significant differences in behavior between both games. Using the strategy method, allows us to explore the motivations leading to those differences. Since each subject played the same version of the game eight rounds against changing anonymous opponents we can also study subjects' learning behavior. We propose a theory of boundedly rational behavior, called the “anticipation philosophy”, which is well supported by the experimental data.

Experimental results on ultimatum games with incomplete information

The theory of global games has shown that coordination games with multiple equilibria may have a unique equilibrium if certain parameters of the payoff function are private information instead of common knowledge. We report the results of an experiment designed to test the predictions of this theory. Comparing sessions with common and private information, we observe only small differences in behavior. For common information, subjects coordinate on threshold strategies that deviate from the global game solution towards the payoff-dominant equilibrium. For private information, thresholds are closer to the global game solution than for common information. Variations in the payoff function affect behavior as predicted by comparative statics of the global game solution. Predictability of coordination points is about the same for both information conditions.

/pdf/the-theory-of-global-games-on-test-experimental-analysis-of-1lveqtrpr5.pdf

Rosemarie Nagel

Papers

Unraveling in Guessing Games: An Experimental Study

Search Dynamics in Consumer Choice under Time Pressure: An Eye-Tracking Study

Neural correlates of depth of strategic reasoning in medial prefrontal cortex

Experimental results on ultimatum games with incomplete information

The theory of global games on test: experimental analysis of coordination games with public and private information