Payoff Difference Research Articles

Enforcement of Contribution Norms in Public Good Games with Heterogeneous Populations

Economic and social interaction takes place between individuals with heterogeneous characteristics. We investigate experimentally the emergence and informal enforcement of different contribution norms to a public good in homogeneous and different heterogeneous groups. When punishment is not allowed all groups converge towards free-riding. With punishment, contributions increase and differ distinctly across groups and individuals with different induced characteristics. We show econometrically that these differences are not accidental but enforced by punishment. The enforced contribution norms are related to fairness ideas of equity regarding contribution possibilities but not regarding earnings. Individuals with different characteristics tacitly agree on the norm to be enforced, even if this leads to large payoff differences. Our results also emphasize the role of details of the environment that may alter focal contribution norms in an important way.

On the elimination of dominated strategies in stochastic models of evolution with large populations

A stochastic myopic best-reply dynamics is said to have property (W), for a given number of players n, if every pure weakly dominated strategy in every n-player game is eliminated in the long-run distribution of play induced by the dynamics. In this paper I give a necessary and sufficient condition that a dynamics has to satisfy in order for it to have property (W). The key determinant is found to be the sensitivity of the learning-rate to small payoff differences, inherent in the dynamics. If this sensitivity is higher than a certain cut-off, which depends on the number of players, then the dynamics satisfies property (W). If it is equal to or below that cut-off, then the dynamics does not satisfy property (W).

Variations in Individual Decision Making: Children, Adults, and Economic Theory

This study examines differences in individual decision making between children and adults using a paired lottery choice experiment. A lottery choice experiment involves selecting between two options, one with a small difference in payoffs and one with a large difference in payoffs, for each of ten decisions with increasing probability of obtaining the higher payoff. Based on subject decisions, risk preferences can be inferred. Particular attention is given to age and gender differences. The main result reveals that children choose significantly fewer “safe” lotteries than adults on average. Specifically, children act as risk-seeking in low winning percentage lotteries. There is no significant difference in safe choices between genders in both samples. These findings can prove to be an important asset when developing policies to curb hazardous behavior in children.

On the existence of pure-strategy perfect equilibrium in discontinuous games

We provide sufficient conditions for a (possibly) discontinuous normal-form game to possess a pure-strategy trembling-hand perfect equilibrium. We first show that compactness, continuity, and quasiconcavity of a game are too weak to warrant the existence of a pure-strategy perfect equilibrium. We then identify two classes of games for which the existence of a pure-strategy perfect equilibrium can be established: (1) the class of compact, metric, concave games satisfying upper semicontinuity of the sum of payoffs and a strengthening of payoff security; and (2) the class of compact, metric games satisfying upper semicontinuity of the sum of payoffs, strengthenings of payoff security and quasiconcavity, and a notion of local concavity and boundedness of payoff differences on certain subdomains of a player's payoff function. Various economic games illustrate our results.

Detecting the effects of selection and stochastic forces in archaeological assemblages

Detecting and diagnosing the causes of change through time in archaeological assemblages is a core enterprise of archaeology. Evolutionary approaches to this problem typically cast the causes of culture change as being either stochastic in origin, or arising from selection. Stochastic sources of change include random innovations, copying errors, drift and founder effects among dispersing groups. Selection is driven by differences in payoffs between cultural variants. Most efforts to identify these evolutionary forces in the archaeological record have relied on assessing how well the predictions from a neutral-stochastic model of cultural transmission fit a data set. Selection is inferred when the neutral-stochastic model fits poorly. A problem with this approach is that it does not test directly for the presence selection. Moreover, it does not account for the fact that both neutral-stochastic and selective forces can act at the same time on the same cultural variants. A different approach based on the Price Equation allows for the simultaneous measurement of selective and stochastic forces. This paper extends use of the Price Equation to the analysis of selective and stochastic forces operating on multiple artifact types within an assemblage. Ceramic data presented by Steele et al. (2010, Vol. 37(6): 1348–1358) from the Late Bronze Age Hittite site of Boğazköy-Hattusa, Turkey, provide an opportunity to evaluate the efficacy of this model. The results suggest that selection is a dominant process driving the frequency evolution of different bowl rim types within the assemblage and that stochastic forces played little or no role. It is also clear, however, that we should be attentive to combinations of direct and indirect selective effects within assemblages consisting of multiple artifact types.

Similarities and differences when building trust: the role of cultures

We run an experiment in which students of different European nationalities are matched in groups of five and repeatedly choose with whom within their group they want to play a trust game. Participants observe of each other age, gender, nationality and number of siblings. The region of origin, “North” or “South” is a major determinant of success in the experiment. Participants tend to trust those they trusted before and who trusted them. We do not find evidence of regional discrimination per se. It is only the underlying and significant differences in behavior that translate through repeated interactions into differences in payoffs between the two regions.

The monoclus of a coalitional game

The analysis of single-valued solution concepts, providing payoffs to players for the grand coalition only, has a long tradition. Opposed to most of this literature we analyze allocation scheme rules, which assign payoffs to all players in all coalitions. We introduce several closely related allocation scheme rules, each resulting in a population monotonic allocation scheme (PMAS) whenever the underlying coalitional game with transferable utilities has a PMAS. Monotonicities, which measure the payoff difference for a player between two nested coalitions, are the driving force. These monotonicities can best be compared with the excesses in the definition of the (pre-)nucleolus. Variants are obtained by considering different domains and/or different collections of monotonicities. We deal with nonemptiness, uniqueness, and continuity, followed by an analysis of conditions for (some of) the rules to coincide. We then focus on characterizing the rules in terms of subbalanced weights. Finally, we deal with computational issues.

You Don't Want To Know What You're Missing: When Information about Forgone Rewards Impedes Dynamic Decision Making

Event Abstract Back to Event You Don't Want To Know What You're Missing: When Information about Forgone Rewards Impedes Dynamic Decision Making A. R. Otto1* and Bradley C. Love1 1 University of Texas, United States In simple delay-of-gratification paradigms, diverting one’s attention from immediate rewards is an effective self-control strategy for refraining from short-term gains in order to maximize larger, long-term gains. These findings suggest that knowledge about foregone rewards (i.e., what could have been gained at each point by making a different choice) may impede long-term optimal decisions during intertemporal choice. We examined the effect of information about foregone rewards in a two-choice dynamic decision-making task in which short- and long-term gains were in conflict. In our task, participants made choices for real money. We found that providing veridical information about foregone rewards severely hindered participants’ ability to repeatedly make choices that maximize long-term rewards. In other words, we obtained a surprising pattern of results suggesting that the addition of relevant information in our task can lead to globally suboptimal choice patterns. We found that participants’ choice behavior is well characterized by a single Reinforcement-Learning (RL) mechanism that learns from both directly experienced and foregone rewards. This RL model predicts the deleterious effect of veridical information about foregone rewards. Further, individual differences in choice performance are elucidated by parameter fits, which lends support to the view that increased attention to foregone rewards accentuates the salience of immediate payoff differences between short- and long-term options. Conference: Computations, Decisions and Movement, Giessen, Germany, 19 May - 22 May, 2010. Presentation Type: Poster Presentation Topic: Posters Citation: Otto AR and Love BC (2010). You Don't Want To Know What You're Missing: When Information about Forgone Rewards Impedes Dynamic Decision Making. Front. Comput. Neurosci. Conference Abstract: Computations, Decisions and Movement. doi: 10.3389/conf.fnins.2010.01.00013 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 01 Feb 2010; Published Online: 01 Feb 2010. * Correspondence: A. R Otto, University of Texas, Austin, United States, rotto@nyu.edu Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers A. R Otto Bradley C Love Google A. R Otto Bradley C Love Google Scholar A. R Otto Bradley C Love PubMed A. R Otto Bradley C Love Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

The Neural Circuitry of a Broken Promise

Promises are one of the oldest human-specific psychological mechanisms fostering cooperation and trust. Here, we study the neural underpinnings of promise keeping and promise breaking. Subjects first make a promise decision (promise stage), then they anticipate whether the promise affects the interaction partner's decision (anticipation stage) and are subsequently free to keep or break the promise (decision stage). Findings revealed that the breaking of the promise is associated with increased activation in the DLPFC, ACC, and amygdala, suggesting that the dishonest act involves an emotional conflict due to the suppression of the honest response. Moreover, the breach of the promise can be predicted by a perfidious brain activity pattern (anterior insula, ACC, inferior frontal gyrus) during the promise and anticipation stage, indicating that brain measurements may reveal malevolent intentions before dishonest or deceitful acts are actually committed.

Brood sex ratio does not affect helper effort in a cooperative bird, despite extreme sex-biased dispersal

Among vertebrates, particularly birds, evidence for facultative adjustment of brood sex ratios is inconsistent. Results from cooperatively breeding species are clearer, where sex-biased dispersal and helping behaviour may accentuate any differences in fitness payoffs to parents of raising sons versus daughters. We might expect similar payoff differences for cooperative helpers raising offspring of each sex, but this has rarely been tested. Bell miners, Manorina melanophrys, are known to adjust their primary brood sex ratio according to habitat productivity. Helpers of both sexes provision broods even when unrelated to offspring, which indicates the potential importance of direct fitness benefits (e.g. group augmentation) that should depend heavily on offspring sex. As only females disperse, we anticipated helpers would invest more heavily in male-biased broods, particularly if they were unrelated to broods and thus not gaining indirect benefits. Helpers did feed all-male broods at a greater rate, although, contrary to expectations, this was the result of higher levels of effort by related and not unrelated helpers, irrespective of helper sex. The subsequent interaction between relatedness and brood sex ratio was also an exclusively between-subjects effect, and not due to any within-subject facultative adjustment by individual helpers feeding at multiple nests. Furthermore, the acoustic characteristics of nestling begging calls showed no reliable sex differences; thus helpers probably lacked accurate information on nestling sex to make facultative adjustments according to brood sex ratio. Additional work examining these kinds of trade-offs in other cooperative species where sons and daughters yield differing payoffs to helpers is warranted.

Selection of noise level in strategy adoption for spatial social dilemmas

We studied spatial Prisoner's Dilemma and Stag Hunt games where both the strategy distribution and the players' individual noise level could evolve to reach higher individual payoff. Players are located on the sites of different two-dimensional lattices and gain their payoff from games with their neighbors by choosing unconditional cooperation or defection. The way of strategy adoption can be characterized by a single K (temperaturelike) parameter describing how strongly adoptions depend on the payoff difference. If we start the system from a random strategy distribution with many different player specific K parameters, the simultaneous evolution of strategies and K parameters drives the system to a final stationary state where only one K value remains. In the coexistence phase of cooperator and defector strategies the surviving K parameter is in good agreement with the noise level that ensures the highest cooperation level if uniform K is supposed for all players. In this paper we give a thorough overview about the properties of this evolutionary process.

Cooperation and charity in spatial public goods game under different strategy update rules

Human cooperation can be influenced by other human behaviors and recent years have witnessed the flourishing of studying the coevolution of cooperation and punishment, yet the common behavior of charity is seldom considered in game-theoretical models. In this article, we investigate the coevolution of altruistic cooperation and egalitarian charity in spatial public goods game, by considering charity as the behavior of reducing inter-individual payoff differences. Our model is that, in each generation of the evolution, individuals play games first and accumulate payoff benefits, and then each egalitarian makes a charity donation by payoff transfer in its neighborhood. To study the individual-level evolutionary dynamics, we adopt different strategy update rules and investigate their effects on charity and cooperation. These rules can be classified into two global rules: random selection rule in which individuals randomly update strategies, and threshold selection rule where only those with payoffs below a threshold update strategies. Simulation results show that random selection enhances the cooperation level, while threshold selection lowers the threshold of the multiplication factor to maintain cooperation. When charity is considered, it is incapable in promoting cooperation under random selection, whereas it promotes cooperation under threshold selection. Interestingly, the evolution of charity strongly depends on the dispersion of payoff acquisitions of the population, which agrees with previous results. Our work may shed light on understanding human egalitarianism.

Positional learning with noise

We propose (and test experimentally) a model of observational learning in which players have social preferences. To this end, we design an experiment–based on a classic parlor game known as the Chinos Game–in which we vary (by way of an exogenous iid stochastic process) the probability of getting the prize in the event of a correct guess. By this design, we are able to estimate more efficiently players’ sensitivity to difference in payoffs (and how this sensitivity affects information decoding along the sequence). We also condition our estimates upon additional information on subjects’ socio-demographics, risk attitudes and cognitive reflection by way of a questionnaire that we collect at the end of each session.

Effects of strategy-migration direction and noise in the evolutionary spatial prisoner’s dilemma

Spatial games are crucial for understanding patterns of cooperation in nature (and to some extent society). They are known to be more sensitive to local symmetries than, e.g., spin models. This paper concerns the evolution of the prisoner's dilemma game on regular lattices with three different types of neighborhoods--the von Neumann, Moore, and kagomé types. We investigate two kinds of dynamics for the players to update their strategies (that can be unconditional cooperator or defector). Depending on the payoff difference, an individual can adopt the strategy of a random neighbor [a voter-model-like dynamics (VMLD)] or impose its strategy on a random neighbor, i.e., invasion-process-like dynamics (IPLD). In particular, we focus on the effects of noise, in combination with the strategy dynamics, on the evolution of cooperation. We find that VMLD, compared to IPLD, better supports the spreading and sustaining of cooperation. We see that noise has nontrivial effects on the evolution of cooperation: maximum cooperation density can be realized either at a medium noise level, in the limit of zero noise or in both these regions. The temptation to defect and the local interaction structure determine the outcome. Especially, in the low noise limit, the local interaction plays a crucial role in determining the fate of cooperators. We elucidate these both by numerical simulations and mean-field cluster approximation methods.

Allocation of effort as a function of payoffs for individual tasks in a multitasking environment

SYNWORK1 software allows the examination of how payoffs affect the allocation of effort by people when they perform four different tasks (memory search, arithmetic, visual monitoring, and auditory monitoring). In a previous study (Wang, Proctor, & Pick, 2007), we showed that participants adopted multitasking strategies allocating relative effort appropriate to payoff differences between the arithmetic and memory tasks, but that they exhibited residual effects of prior payoffs when the payoffs were switched. In the present study, we varied the payoff in two different experiments for only one of these tasks, the memory task in Experiment 1 and the arithmetic task in Experiment 2. Doing this allowed consideration of performance for both the task for which payoff changed explicitly and the other cognitive task, for which the payoff difference was implicit (i.e., relative to the explicit payoff that was manipulated). Although participants adjusted performance on the task for which the payoff explicitly varied, the payoff manipulation had less effect than did the explicit payoff manipulations for both tasks used previously. Also, the change in effort on a task resulting from explicitly increasing its payoff was less than that from decreasing the payoff. SYNWORK1 is a good environment for studying multitasking, but has several limitations that need to be addressed to provide a synthetic work environment that allows investigation of a wider range of theoretically relevant issues.

Not it: opting out of voluntary coalitions that provide a public good

Most coalitions that form to increase contributions to a public good do not require full participation by all users of the public good, and therefore create incentives for free riding. If given the opportunity to opt out of a voluntary coalition, in theory, agents should try to be among the first to do so, forcing the remaining undecided agents to bear the cost of participating in the coalition. This study tests the predicted sequence of participation decisions in voluntary coalitions using real-time threshold public goods experiments. We find that subjects’ behavior is more consistent with the theoretical predictions when the difference in payoffs between coalition members and free-riding non-members is relatively large.

Building Trust One Gift at a Time

This paper reports an experiment evaluating the effect of gift giving on building trust in a relationship. We have nested our explorations in the standard version of the investment game. Our gift treatment includes a dictator stage in which the trustee decides whether to give a gift to the trustor before both of them proceed to play the investment game. We observe that in such case the majority of trustees offer their endowment to trustors. Consequently, receiving a gift significantly increases the amounts sent by trustors when controlling for the differences in payoffs created by it. Trustees are, however, not better off by giving a gift as the increase in the amount sent by trustors is not large enough to offset the trustees’ loss associated with the cost of giving a gift. Our results indicate that a relationship which is initiated by gift giving leads to higher trust and efficiency but at the same time is probably not stable.

Diversity-optimized cooperation on complex networks

We propose a strategy for achieving maximum cooperation in evolutionary games on complex networks. Each individual is assigned a weight that is proportional to the power of its degree, where the exponent alpha is an adjustable parameter that controls the level of diversity among individuals in the network. During the evolution, every individual chooses one of its neighbors as a reference with a probability proportional to the weight of the neighbor, and updates its strategy depending on their payoff difference. It is found that there exists an optimal value of alpha, for which the level of cooperation reaches maximum. This phenomenon indicates that, although high-degree individuals play a prominent role in maintaining the cooperation, too strong influences from the hubs may counterintuitively inhibit the diffusion of cooperation. Other pertinent quantities such as the payoff, the cooperator density as a function of the degree, and the payoff distribution are also investigated computationally and theoretically. Our results suggest that in order to achieve strong cooperation on a complex network, individuals should learn more frequently from neighbors with higher degrees, but only to a certain extent.

Motion of influential players can support cooperation in Prisoner’s Dilemma

We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor's strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategy therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densities.

Cooperation in spatial prisoner’s dilemma with two types of players for increasing number of neighbors

We study a spatial two-strategy (cooperation and defection) prisoner's dilemma game with two types ( A and B ) of players located on the sites of a square lattice. The evolution of strategy distribution is governed by iterated strategy adoption from a randomly selected neighbor with a probability depending on the payoff difference and also on the type of the neighbor. The strategy adoption probability is reduced by a prefactor (w<1) from the players of type B . We consider the competition between two opposite effects when increasing the number of neighbors ( k=4 , 8, and 24). Within a range of the portion of influential players (type A ) the inhomogeneous activity in strategy transfer yields a relevant increase (dependent on w ) in the density of cooperators. The noise dependence of this phenomenon is also discussed by evaluating phase diagrams.