Individual Heterogeneity in Punishment and Reward

We design experiments to study the extent to which individuals differ in their motivations behind costly punishment and rewarding. Our findings qualify existing evidence and suggest that the largest fraction of players is motivated by a mixture of both inequity-aversion and reciprocity, while smaller fractions are primarily motivated by pure inequity-aversion and pure reciprocity. These findings provide new insights into the literature on other-regarding preferences and may help to reconcile important phenomena reported in the experimental literature on punishment and reward.Heterogeneity; inequity aversion; monetary punishment/reward; reciprocity; social norms.

Learning in experimental 2×2 games

In this paper we introduce four new learning models: impulse balance learning, impulse matching learning, action-sampling learning, and payoff-sampling learning. With this models and together with the models of self- tuning EWA learning and reinforcement learning, we conduct simulations over 12 different 2×2 games and compare the results with experimental data obtained by Selten & Chmura (2008). Our results are two-fold: While the simulations, especially those with action-sampling learning and impulse matching learning successfully replicate the experimental data on the aggregate, they fail in describing the individual behavior. A simple inertia rule beats the learning models in describing individuals behavior.Learning, Action-sampling, Payo?-sampling, Impulse balance, Impulse matching, Reinforcement, self-tuning EWA, 2×2 games, Experimental data

Games on graphs: A minor modification of payoff scheme makes a big difference

Various social dilemma games that follow different strategy updating rules have been studied on many networks.The reported results span the entire spectrum, from significantly boosting,to marginally affecting,to seriously decreasing the level of cooperation.Experimental results that are qualitatively different from theoretical prediction have also been reported.It is widely believed that the results are largely determined by three elements,including payoff matrices of the underlying 2*2 games,the way that the strategic states of the players are updated and the structure of the networks.Here we discuss the impact of a seemly non-essential mechanism -- what we refer to as a "payoff scheme". Specifically, in each round after the states of all of the players are determined,the payoff scheme is how each player's payoff is calculated.In addition to the two conventions in which either the accumulated or the averaged payoff is calculated from playing with all of the neighboring players,we here study the effects of calculating the payoff from pairing up with one random player from among the neighboring players. Based on probability theory, in a situation of uncorrelated events, the average payoff that involves all of the neighbors should,in principal,be equivalent to the payoff from pairing up with one neighbor.However,our simulation of games on graphs shows that, in many cases,the two payoff schemes lead to qualitatively different levels of cooperation.This finding appears to provide a possible explanation for a wide spectrum of observed behaviors in the literature.We have also observed that results from the randomly-pairing-one mechanism are more robust than the involving-all-neighbours mechanism because,in the former case, neither the other three main elements nor the initial states of the players have a large impact on the final level of cooperation compared with in the latter case.Comment: 23 pages,171 figure

A Survey of Models of Network Formation: Stability and Efficiency

I survey the recent literature on the formation of networks. I provide definitions of network games, a number of examples of models from the literature, and discuss some of what is known about the (in)compatibility of overall societal welfare with individual incentives to form and sever links

Information, fairness, and efficiency in bargaining

Economic theory assumes people strive for efficient agreements that benefit all consenting parties. The frequency of mutually destructive conflicts such as strikes, litigation, and military conflict, therefore, poses an important challenge to the field

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

The Minority of Three-Game: An Experimental and Theoretical Analysis

We report experimental and theoretical results on the minority of three-game where three players have to choose one of two alternatives independently and the most rewarding alternative is the one chosen by a single player. This coordination game has many asymmetric equilibria in pure strategies that are non strict and payoff-asymmetric, and a unique symmetric mixed strategy equilibrium in which each player's behavior is based on the toss of a fair coin. We show that such a straightforward behavior is predicted by Harsanyi and Selten's (1988) equilibrium selection theory as well as alternative solution concepts like impulse balance equilibrium and sampling equilibrium. Our results indicate that participants rely on various decision rules, and that only a quarter of them decide according to the toss of a fair coin. Reinforcement learning is the most successful decision rule as it describes best the behavior of about a third of our participants.Coordination, Minority game, Mixed strategy, Learning models, Experiments

An Agent-Based Model of Behavior in “Beauty Contest” Games

Recently, computer simulation, particularly agent-based modeling, has grown in popularity as a method to uncover macro patterns and developments that emerge from simple micro behavior. The present paper combines both techniques by using protocol analysis to uncover player strategies in an experiment and encoding those strategies in an agent-based computer simulation. In particular, Keynes’ (1936) beauty contest analogy is simulated in a number-guessing context. Several researchers have conducted experiments asking subjects to play “p-beauty contest games” in order to compare the experimental results with those predicted by the game-theoretic, deductive reasoning concept of iterated dominance. Our results are compared with those found experimentally in order to demonstrate the usefulness of a combining agent-based modeling with protocol analysis.Agent-Based modeling; Beauty contest games