Donation Payment Mechanisms and Contingent Valuation: An Empirical Study of Hypothetical Bias

Donation payment mechanisms are well suited forsome contingent valuation studies. In aneffort to better understand the discrepancythat has been consistently found between actualand hypothetical donations, we investigate anapproach to estimating actual willingness todonate using contingent donations with afollow-up question in which respondents ratethe level of certainty about their response tothe contingent donation question. The approachallows us to estimate the magnitude of thehypothetical bias and identify the respondentsresponsible for the bias. Identification ofthe respondents responsible for thehypothetical bias is the first step towarddeveloping an understanding of the causes andpossible remedies. In this study we find thatmost of the respondents (80%) to thecontingent donation question provide a responseconsistent with how we predict they wouldrespond in an actual donation situation.     

Behavioral spillovers and cognitive load in multiple games: An experimental study

We present evidence from laboratory experiments of behavioral spillovers and cognitive load that spread across strategic contexts. In the experiments, subjects play two distinct games simultaneously with different opponents. We find that the strategies chosen and the efficiency of outcomes in one game depends on the other game that the subject plays, and that play is altered in predictable directions. We develop a measure of behavioral variation in a normal form game, outcome entropy, and find that prevalent strategies in games with low outcome entropy are more likely to be used in the games with high outcome entropy, but not vice versa. Taken together, these findings suggest that people do not treat strategic situations in isolation, but may instead develop heuristics that they apply across games.     

AN EXPERIMENT WITH ULTIMATUM BARGAINING IN A CHANGING ENVIRONMENT*

We present experimental results on the ultimatum bargaining game which support an evolutionary explanation of subjects’ behaviour in the game. In these experiments subjects interacted with each other and also with virtual players, i.e. computer programs with pre‐specified strategies. Some of these virtual players were designed to play the equitable allocation, while others exhibited behaviour closer to the subgame‐perfect equilibrium, in which the proposer's share is much larger than that of the responder. We have observed significant differences in the behaviour of real subjects depending on the type of “mutants” (virtual players) that were present in their environment.     

Higher order game dynamics

Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players? strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces of change, specifying e.g. the acceleration of the players? evolution instead of its velocity (a viewpoint which emerges naturally when it comes to aggregating empirical data of past instances of play). To that end, we derive a wide class of higher order game dynamics, generalizing first order imitative dynamics, and, in particular, the replicator dynamics. We show that strictly dominated strategies become extinct in n-th order payoff-monotonic dynamics n   orders as fast as in the corresponding first order dynamics; furthermore, in stark contrast to first order, weakly dominated strategies also become extinct for n?2$n?2$. All in all, higher order payoff-monotonic dynamics lead to the elimination of weakly dominated strategies, followed by the iterated deletion of strictly dominated strategies, thus providing a dynamic justification of the well-known epistemic rationalizability process of Dekel and Fudenberg [7]. Finally, we also establish a higher order analogue of the folk theorem of evolutionary game theory, and we show that convergence to strict equilibria in n-th order dynamics is n orders as fast as in first order.     

RISKY VERSUS RISKLESS BARGAINING PROCEDURES: THE AUMANN‐ROTH CONTROVERSY REVISITED*

In a series of papers, Aumann and Roth discussed a game in which players can cooperate in pairs and two of them prefer to form a coalition with each other. Roth argued that the only rational outcome is that the players who prefer each other form a coalition; Aumann argued that all three coalitions are possible because the players have a problem of expectation coordination. A non‐cooperative analysis provides additional support for Aumann's arguments and shows that the difference between Aumann's and Roth's views can be traced back to a difference (risky versus/riskless) in the bargaining procedure.     

Trees and extensive forms

This paper addresses the question of what it takes to obtain a well-defined extensive form game. Without relying on simplifying finiteness or discreteness assumptions, we characterize the class of game trees for which all pure strategy combinations induce unique outcomes. The generality of the set-up covers “exotic” cases, like stochastic games or decision problems in continuous time (differential games). We find that the latter class, though a well-defined problem, fails this test.     

Investigating Donating Behavior Using Hypothetical Dictator Game Experiments

We conduct dictator game experiments to investigate donating behavior by simultaneously examining the time delay when the donee receives the donation and the individual characteristics of the donor. We show that donations decrease as the time delay rises and that gender, education level, neuroticism, agreeableness, conscientiousness, and utilitarianism affect donations independent of the time delay.     

Collusion as public monitoring becomes noisy: Experimental evidence

This paper uses laboratory experiments to test the implications of the theory of repeated games on equilibrium payoffs and estimate strategies in an infinitely repeated prisoners' dilemma game with imperfect public monitoring. We find that subjects' payoffs (i) decrease as noise increases, and (ii) are lower than the theoretical maximum for low noise, but exceed it for high noise. Under the assumption that the subjects' strategy uses thresholds on the public signal for transition between cooperation and punishment states, we find that the best fitting strategy simply compares the most recent public signal against a single threshold.     

Coexistence of Strategies and Culturally-Specific Common Knowledge: An Evolutionary Analysis

We analyze social dynamics in a continuous population where randomly matched individuals have to choose between two pure strategies only ('cooperate' (C) and 'not cooperate' (NC)). Individual payoffs associated with the possible outcomes of each interaction may differ across groups, depending on the specific social and cultural context to which each agent belongs. In particular, it is assumed that three sub-populations are initially present, 'framing' the game according to the prisoner's dilemma (PD), assurance game (AG) and other regarding (OR) payoff configurations, respectively. In other words, we assume that common knowledge about the payoffs of the game is 'culturally-specific'. In this context, we examine both the adoption process of strategies C and NC within each sub-population and the diffusion process of 'types' (PD, AG and OR) within the overall community. On the basis of an evolutionary game-theoretic approach, the paper focuses on the problem of coexistence of PD, AG and OR groups as well as of 'nice' (C) and 'mean' (NC) strategies. We show that coexistence between C and NC is possible in the heterogeneous community under examination, even if it is ruled out in homogeneous communities where only one of the three types is present. This revised version was published online in July 2006 with corrections to the Cover Date.     

Conditional cooperation in a sequential move game

Cooperation is a pervasive social phenomenon, but more often than not economic theories have little to say about its causes and consequences. In this paper, we explore the hypothesis that cooperative behaviour might be motivated by pure self-interest when the “social” payoff in a game is increasing. We report the results of a series of experiments on the Centipede game. The experiments are organised in two subsequent steps. Subjects first participate in a 2-period trust game, randomly matched with unknown partners. We apply the strategy method in order to elicit their social preferences. On the basis of their pre-game behaviour, individuals are divided into three main social groups: selfish individuals, pure altruists and reciprocators. At the second step of the experiment, subjects play a repeated 6-move Centipede game with an increasing final payoff. Each subject plays twice, in a low and in a high-stake Centipede game, and he/she is informed about his/her co-player social preferences. We provide statistical evidence to identify the origin of cooperation within homogeneous and heterogeneous social groups. We construct a Poisson regression model to assess the determinants of the duration of conditional cooperation in the Centipede.     

Do people behave in experiments as in the field?—evidence from donations

Laboratory experiments are an important methodology in economics, especially in the field of behavioral economics. However, it is still debated to what extent results from laboratory experiments are informative about behavior in field settings. One highly important question about the external validity of experiments is whether the same individuals act in experiments as they would in the field. This paper presents evidence on how individuals behave in donation experiments and how the same individuals behave in a naturally occurring decision situation on charitable giving. While we find evidence that pro-social behavior is more accentuated in the lab, the data show that pro-social behavior in experiments is correlated with behavior in the field.      

Experimental study of repeated team-games

We report an experiment in which the Intergroup Prisoner's Dilemma (IPD) game was contrasted with a structurally identical (single-group) Prisoner's Dilemma (PD). The games were played repeatedly for 40 rounds. We found that subjects were initially more likely to cooperate in the IPD game than in the PD game. However, cooperation rates decreased as the game progressed and, as a result, the differences between the two games disappeared. This pattern is consistent with the hypothesis that subjects learn the structure of the game and adapt their behavior accordingly. Computer simulations based on a simple learning model by Roth and Erev (Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term, Games and Economic Behavior 8, 164–212, 1995) support this interpretation.     

The control of game form recognition in experiments: understanding dominant strategy failures in a simple two person “guessing” game

This paper focuses on instructions and procedures as the reasons that subjects fail to behave according to the predictions of game theory in two-person “guessing game” (beauty contest game) experiments. In this game, two individuals simultaneously choose a number between 0 and 100. The winner is the person whose chosen number is the closest to 2/3 of the average of the two numbers. The weakly dominant strategy is zero. Because of the simplicity of the game, the widespread failure of subjects to choose the weakly dominant strategy has been interpreted as evidence of some fundamental inability to behave strategically. By contrast, we find that subjects’ behavior reflects a lack of understanding of the game form, which we define as the relationships between possible choices, outcomes and payoffs. To a surprising degree, subjects seem to have little understanding of the experimental environment in which they are participating. If subjects do not understand the game form, the experimental control needed for testing game theory is lost. The experiments reported here demonstrate that the failure to act strategically is related to how the game is presented. We test how well subjects are able to recognize the game under a variety of different presentations of the game. Some subjects fail to recognize the game form when it is presented abstractly. When the game is transformed into a simple isomorphic game and presented in a familiar context, subjects do choose weakly dominant strategies. While our results confirm the ability of subjects to make strategic decisions, they also emphasize the need to understand the limitations of experimental subjects’ ability to grasp the game as the experimenter intends. Given these limitations, we provide suggestions for better experimental control.     

Testing the TASP: An experimental investigation of learning in games with unstable equilibria

We report experiments studying mixed strategy Nash equilibria that are theoretically stable or unstable under learning. The Time Average Shapley Polygon (TASP) predicts behavior in the unstable case. We study two versions of Rock-Paper-Scissors that include a fourth strategy, Dumb. The unique Nash equilibrium is identical in the two games, but the predicted frequency of Dumb is much higher in the game where the NE is stable. Consistent with TASP, the observed frequency of Dumb is lower and play is further from Nash in the high payoff unstable treatment. However, Dumb is played too frequently in all treatments.     

Anonymity in the dictator game revisited

Giving in the dictator game has often been interpreted as evidence of other-regarding preferences. We suspect that giving is determined by subjects’ attempts to appear fair in the eyes of recipients and the experimenter. Therefore, we investigate behavior in the dictator game by using the randomized response technique to increase anonymity. Overall, 290 subjects participated in two experiments. The results demonstrate that the randomized response technique reduces giving to negligible amounts compared to the standard double blind condition. Thus, our results suggest that individuals closely follow egoistic motives in the dictator game when anonymity is convincingly implemented.     

Cooperation,Trust and Economic Development: An Experimental Study in China

Many previous empirical studies have suggested that cooperation and trust affect economic growth. However, the precise relationship between trust and cooperation (i.e. whether trust leads to cooperation or cooperation leads to trust) remains unclear and it is not known how the level of economic development affects the level of cooperation and trust. Using a combination of public goods, gambling game and trust game experiments, we investigate the links among cooperation, trust and economic development in four regions of China. Our results suggest that, first, there is a U‐shaped or V‐shaped relationship between cooperation and economic development. Second, on the one hand, cooperation leads to trust, and on the other hand, more cooperative behaviour may be created by rewarding trusting behaviour. Third, men are more cooperative and trusting than women. Furthermore, we find that the widely used ‘GSS trust’ question from the General Social Survey (GSS) does not predict either cooperation or trust, whereas the questions ‘GSS fair’ and ‘GSS help’ have weak predictive power for trusting behaviour but not for cooperative behaviour.     

Equilibrium play and best response to (stated) beliefs in normal form games

We report experimental results on a series of ten one-shot two-person 3×3 normal form games with unique equilibrium in pure strategies played by non-economists. In contrast to previous experiments in which game theory predictions fail dramatically, a majority of actions taken coincided with the equilibrium prediction (70.2%) and were best-responses to subjects' stated beliefs (67.2%). In constant-sum games, 78% of actions taken were predicted by the equilibrium model, outperforming simple K-level reasoning models. We discuss how non-trivial game characteristics related to risk aversion, efficiency concerns and social preferences may affect the predictive value of different models in simple normal form games.     

Framing and Misperception in Public Good Experiments

Earlier studies have found that framing has a substantial impact on the degree of cooperation observed in public good experiments. We show that the way the public good game is framed affects misperceptions about the incentives of the game. Moreover, we show that such framing‐induced differences in misperceptions are linked to the framing effect on subjects' cooperation behavior. When we do not control for the different levels of misperceptions between frames, we observe a significant framing effect on subjects' cooperation preferences. However, this framing effect becomes insignificant once we remove subjects who misperceive.     

Are we nice(r) to nice(r) people?—An experimental analysis

We experimentally investigate whether individuals can reliably detect cooperators (the nice(r) people) in an anonymous decision environment involving “connected games.” Participants can condition their choices in an asymmetric prisoners’ dilemma and a trust game on past individual (their partner’s donation share to a self-selected charity) and social (whether their partner belongs to a group with high or low average donations) information. Thus, the two measures of niceness are the individual donation share in the donation task, and the cooperativeness of one’s choice in the two games. We find that high donors achieve a higher-than-average expected payoff by cooperating predominantly with other high donors. Group affiliation proved to be irrelevant. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C91, C72, D3