Games, Volume 9, Issue 4 (December 2018) – 31 articles

Different strains of influenza viruses spread in human populations during every epidemic season. As the size of an infected population increases, the virus can mutate itself and grow in strength. The traditional epidemic SIR model does not capture virus mutations and, hence, the model is not sufficient to study epidemics where the virus mutates at the same time as it spreads. In this work, we establish a novel framework to study the epidemic process with mutations of influenza viruses, which couples the SIR model with replicator dynamics used for describing virus mutations. We formulated an optimal control problem to study the optimal strategies for medical treatment and quarantine decisions. We obtained structural results for the optimal strategies and used numerical examples to corroborate our results. Full article

We formally explore the idea that punishment of norm-breakers may be a vehicle for the older generation to teach youngsters about social norms. We show that this signaling role provides sufficient incentives to sustain costly punishing behavior. People punish norm-breakers to pass information about past history to the younger generation. This creates a link between past, present, and future punishment. Information about the past is important for youngsters, because the past shapes the future. Reward-based mechanisms may also work and are welfare superior to punishment-based ones. However, reward-based mechanisms are fragile, since punishment is a more compelling signaling device (in a sense that we make precise). Full article

We conducted a dynamic common pool resource experiment and found large differences among groups in the total benefits (surplus) obtained from the resource. To shed light on the factors underlying the differences, we characterized individual appropriation decisions as irresponsible, sustainable, or constructive, and defined a measure of the intensity of such actions. We then examined the relationships between group-level success and the frequency and intensity of the individual actions, finding that the average intensity of irresponsible actions was the best predictor of group success. We interpreted this as suggestive evidence that policies aimed at preserving and maximizing the benefits of renewable resources should above all else aim to reduce the intensity of irresponsible actions. Full article

Evolution of cooperation by reciprocity has been studied using two-player and n-player repeated prisoner’s dilemma games. An interesting feature specific to the n-player case is that players can vary in generosity, or how many defections they tolerate in a given round of a repeated game. Reciprocators are quicker to detect defectors to withdraw further cooperation when less generous, and better at maintaining a long-term cooperation in the presence of rare defectors when more generous. A previous analysis on a stochastic evolutionary model of the n-player repeated prisoner’s dilemma has shown that the fixation probability of a single reciprocator in a population of defectors can be maximized for a moderate level of generosity. However, the analysis is limited in that it considers only tit-for-tat-type reciprocators within the conventional linear payoff assumption. Here we extend the previous study by removing these limitations and show that, if the games are repeated sufficiently many times, considering non-tit-for-tat type strategies does not alter the previous results, while the introduction of non-linear payoffs sometimes does. In particular, under certain conditions, the fixation probability is maximized for a “paradoxical” strategy, which cooperates in the presence of fewer cooperating opponents than in other situations in which it defects. Full article

The current study aims to investigate how the presence of social norms defines belief formation on future changes in social identity (i.e., diachronic identity), and how those beliefs affect individual decisions under uncertainty. The paper proposes a theoretical model in which individuals have preferences over their own attributes and over specific information structures. The individual preferences are motivated by the presence of social norms. The norms, while establishing the socially acceptable attributes of an individual identity, also drive individuals’ preferences for information acquisition or avoidance. The model incorporates social norms as empirical expectations and provides a prior dependent theory that allows for prior-dependent information attitudes. Firstly, the model implies that decisions are mitigated by socially grounded behavioral and cognitive biases; and secondly, that it can create an incentive to avoid information, even when the latter is useful, free, and independent of strategic considerations. These biases bring out individual trade-offs between the accuracy of decision making and self-image motivated by social conformity. The two behavioral motivations are represented through a game of an intra-personal model of choice under uncertainty in which self-deception and memory manipulation mechanisms are used to overcome the individuals’ internal trade-off. Full article

We studied gender diversity and performance in endogenously formed teams in a repeated teamwork setting. In our experiment, the participants (N = 168, 84 women and 84 men) chose whether to perform a cooperative task only with members of the own gender or in a mixed-gender team. We found that independent of the choice of team, in the initial period, men contributed significantly more to the team projects than women. Men preferred the successful men-only teams in the subsequent periods, resulting in significantly higher profits for men compared to women. This endogenously emerging “gender pay gap” only closed over time. Full article

This paper analyzes the equilibrium strength of prescriptive norms to contribute to public goods. We consider three methods of establishing what an acceptable contribution to the public good is. Under the first method, the contribution of the bottom contributor is the reference point by which the comparison is being made; under the second, the median contribution is the reference point; and under the third the top contribution is the reference. The first method results in a unique equilibrium and the reference contribution is endogenously low. Each of the latter two methods allows for multiple equilibria differing in contributions made and thus in the strength of the norm to contribute. Comparing the methods we show that the median reference allows for the highest equilibrium contributions and welfare of all methods hence is the preferred method if, among the multiple equilibria, the best one can be selected. However, the bottom-reference is the maximin method, i.e., it provides safe minimal aggregate contribution and welfare that surpass the worst outcome in the other two methods. Full article

We explore how subjects with heterogeneous beliefs respond to a surprise restart in a linear public goods game played for 20 rounds using either a “partners” or a “strangers” protocol. There are two restarts: one prior to Round 11 and another prior to Round 16. We elicit subject beliefs at the outset and classify subjects into three groups—Top, Middle, and Bottom—depending on their prior beliefs about their peers’ contributions to the public good. Then, we look at how these three groups respond, in terms of their beliefs and contributions, before and after the restart. We replicate the restart effect, but find that (i) it is much more pronounced for partner matching than for stranger matching and (ii) it is less pronounced in treatments with belief elicitation compared to control treatments where beliefs are not elicited. We also find that the restart has the effect of regenerating a sense of optimism among the subjects, which is reflected in increased contributions subsequently. This increase in contribution is driven mostly by those subjects who started the game with relatively more optimistic beliefs. Our results have implications for sustaining cooperation in social dilemma games. Full article

Charities operate at different levels: national, state, or local. We test the effect of the level of the organization on charitable giving in a sample of adults in two Texas communities. Subjects make four charitable giving “dictator game” decisions from a fixed amount of money provided by the experimenter. Three decisions target different charitable organizations, all of which have a disaster-relief mission, but differ in the level of operation. The fourth targets an individual recipient, identified by the local fire department as a victim of a fire. One of the four is selected randomly for payment. Giving is significantly higher to national and local organizations compared to state. We find a higher propensity to donate and larger amount donated to the individual relative to all organizations. Subsequent analysis compares a number of demographic and attitudinal covariates with donations to specific charities. In a second decision, subjects instead indicate which of their four prior decisions they would most prefer to implement. Here we see that a majority of subjects prefer the gift to the individual. Full article

Schosser (Games 2018, 9, 26) claims to have found an alternative solution to design appropriate performance measures than the State-Contingent Relative Benefit Cost Allocation (RBCA) introduced by Ortner et al. (Management Accounting Research 2017, 36, 43–50), which he states is simpler and more powerful. However, this note reveals that the performance measures proposed by Schosser are, in fact, a specific subset of State-Contingent Robust RBCA performance measures and thus do not represent a new solution. Full article

We provide a game-theoretic account of endogenous intrinsic motivation within a principal–agent framework. We explore the incentives of an altruistic principal who, by exerting costly effort, can intrinsically motivate a present-biased agent to exhibit a direct preference for more far-sighted behaviour. We characterize the conditions under which this happens. We show that allowing for endogenous intrinsic motivation generates interesting interplays between exogenous economic incentives and endogenous motivation, including the possibility of crowding out. Our model can be applied in a wide variety of contexts, including public policy, self-control, and cultural transmission. Full article

While preferences for conformity are commonly seen as an important driver of pro-social behaviour, only a small set of previous studies has explicitly tested the behavioural mechanisms underlying this proposition. In this paper, we report on two interconnected experimental studies that jointly provide a more thorough and robust understanding of a causal mechanism that links social information (i.e., information about the generosity of others) to donations via changing the perception of a descriptive social norm. In a modified dictator game, Experiment 1 re-investigates this mechanism adding further robustness to prior results by eliciting choices from a non-student sample and by implementing an additional treatment that controls for potential anchoring effects implied by the methods used in previous investigations. Experiment 2 adds further robustness by investigating the link between social information, (descriptive) norm perception and giving at the individual, rather than the group average, level. We find that an exogenous variation of social information influences beliefs about others’ contributions (descriptive social norm) and, through this channel, actual giving. An exploratory analysis indicates that this causal relationship is differently pronounced among the two sexes. We rule out anchoring effects as a plausible confound in previous investigations. The key findings carry over to the individual level. Full article

In this work, we explore the role of learning dynamics and social norms in human cooperation on networks. We study the model recently introduced in [Physical Review E, 97, 042321 (2018)] that integrates the well-studied Experience Weighted Attraction learning model with some features characterizing human norm psychology, namely the set of cognitive abilities humans have evolved to deal with social norms. We provide further evidence that this extended model—that we refer to as Experience Weighted Attraction with Norm Psychology—closely reproduces cooperative patterns of behavior observed in large-scale experiments with humans. In particular, we provide additional support for the finding that, when deciding to cooperate, humans balance between the choice that returns higher payoffs with the choice in agreement with social norms. In our experiment, agents play a prisoner’s dilemma game on various network structures: (i) a static lattice where agents have a fixed position; (ii) a regular random network where agents have a fixed position; and (iii) a dynamic lattice where agents are randomly re-positioned at each game iteration. Our results show that the network structure does not affect the dynamics of cooperation, which corroborates results of prior laboratory experiments. However, the network structure does seem to affect how individuals balance between their self-interested and normative choices. Full article

Theoretical models on network formation focus mostly on the stability and efficiency of equilibria, but they cannot deliver an understanding of why specific equilibrium networks are selected or whether they are all actually reachable from any starting network. To study factors affecting equilibrium selection, we designed a network formation experiment with multiple equilibria, which can be categorized in terms of the demand on players’ farsightedness and robustness to errors. In a second scenario, we increase the need for farsighted behavior by players, as well as the perceived riskiness of equilibria by adding a stage in which the network is disrupted. This setting allows us to analyze the interplay between the need for farsightedness and perceived risk of errors and its effect on network formation and equilibrium selection. Full article

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum, non-cooperating, differential games where the players’ state dynamics solve backward stochastic differential equations (BSDE) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters. Full article

Evolution of cooperation has traditionally been studied by assuming that individuals adopt either of two pure strategies, to cooperate or defect. Recent work has considered continuous cooperative investments, turning full cooperation and full defection into two opposing ends of a spectrum and sometimes allowing for the emergence of the traditionally-studied pure strategies through evolutionary diversification. These studies have typically assumed a well-mixed population in which individuals are encountered with equal probability. Here, we allow for the possibility of assortative interactions by assuming that, with specified probabilities, an individual interacts with one or more other individuals of the same strategy. A closely related assumption has previously been made in evolutionary game theory and has been interpreted in terms of relatedness. We systematically study the effect of relatedness and find, among other conclusions, that the scope for evolutionary branching is reduced by either higher average degree of, or higher uncertainty in, relatedness with interaction partners. We also determine how different types of non-linear dependencies of benefits and costs constrain the types of evolutionary outcomes that can occur. While our results overall corroborate the conclusions of earlier studies, i.e. higher relatedness promotes the evolution of cooperation, our investigation gives a comprehensive picture of how relatedness affects the evolution of cooperation with continuous investments. Full article

In impunity games proposers, like allocators in dictator games, can take what they want; however, responders can refuse offers deemed unsatisfactory at own cost. We modify the impunity game via allowing offers to condition of another participant’s counterfactual generosity intention. For a given pair of proposer candidates each states, via the strategy vector method, an intended and two adjusted offers: one (possibly) upward adjusted in case the intended offer of the other candidate is higher and one (possibly) downward adjusted in case it is lower. Additionally, each candidate determines an acceptance threshold for the responder role. Only one candidate in each pair is randomly selected and endowed as the actual proposer whose offer is either possibly upward or downward adjusted depending on the counterfactual offer of the other proposer candidate. The endowed proposer of one pair is matched with the non-endowed candidate of another pair in the responder role. The data confirm that counterfactual intentions of others often affect own generosity via substantial and significant average adjustments to the weakest social influence. Overall, offers seem correlated with acceptance thresholds. Furthermore, we find significant gender differences: female participants state lower intended and adjusted offers as well as acceptance thresholds and therefore appear to be less sensitive to social influence. Full article

We show that a Bayesian game where the type space of each agent is a bounded set of m-dimensional vectors with non-negative components and the utility of each agent depends linearly on its own type only is equivalent to a simultaneous competition in m basic games which is called a uniform multigame. The type space of each agent can be normalised to be given by the $(m-1)$ -dimensional simplex. This class of m-dimensional Bayesian games, via their equivalence with uniform multigames, can model decision making in multi-environments in a variety of circumstances, including decision making in multi-markets and decision making when there are both material and social utilities for agents as in the Prisoner’s Dilemma and the Trust Game. We show that, if a uniform multigame in which the action set of each agent consists of one Nash equilibrium inducing action per basic game has a pure ex post Nash equilibrium on the boundary of its type profile space, then it has a pure ex post Nash equilibrium on the whole type profile space. We then develop an algorithm, linear in the number of types of the agents in such a multigame, which tests if a pure ex post Nash equilibrium on the vertices of the type profile space can be extended to a pure ex post Nash equilibrium on the boundary of its type profile space in which case we obtain a pure ex post Nash equilibrium for the multigame. Full article

We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type which are pure jump processes obtained as solutions of a well-posed martingale problem. As an illustration, we apply the result to generic examples of control problems as well as some applications. Full article

Field studies of networks have uncovered a preference to befriend people we perceive as similar according to some dimensions of our identity (“homophily”). Lab studies of network formation games have found that adherence to social norms of reciprocity and inequity aversion are also drivers of network choices. No study so far has attempted to investigate the role of both homophily and social norms in a controlled environment. At the beginning of our experiment, each player fills in a personal profile. Each player then views the profile of all other players and expresses a degree of perceived similarity between his/her profile and the profile of the other player. At this point, a repeated network formation game ensues. We find that: (1) potential homophily considerations triggered by the profile rating task did not measurably change the players’ behavior compared to the baseline; (2) reciprocity plays a significant role in the formulation of the players’ strategies, in particular lowering the probability that the player naively best responds to the network observed in the previous period. We speculate that reciprocation of past choices might be a more “available” aid in strategy-formulation than considerations related to the similarity of the other players. Full article

We study the determinants of borrowers’ default in P2P lending with a new data set consisting of 70,673 loan observations from the Lending Club. Previous research identified a number of default determining variables but did not distinguish between different loan risk levels. We define four loan risk classes and test the significance of the default determining variables within each loan risk class. Our findings suggest that the significance of most variables depends on the loan risk class. Only a few variables are consistently significant across all risk classes. The debt-to-income ratio, inquiries in the past six months and a loan intended for a small business are positively correlated with the default rate. Annual income and credit card as loan purpose are negatively correlated. Full article

This paper introduces a strategic element into the dictator game by allowing recipients to select their dictator. Recipients are presented with the photographs of two dictators and the envelopes containing their allocations, and are then asked to select which dictator’s gift they would like to receive. The recipient is paid the contents of the envelope they select. The photographs carry information about the gender and race/ethnicity of the dictators, and we ask an independent sample of raters to evaluate the photographs for other characteristics. While gender and ethnicity do not affect the recipient’s choice, one characteristic inferred from the photos makes them significantly more likely to be selected: Their perceived reliability. Full article

In terms of role assignment and informational characteristics, different contexts have been used when measuring distributional preferences. This could be problematic as contextual variance may inadvertently muddle the measurement process. We use a within-subjects design and systemically vary role assignment as well as the way information is displayed to subjects when measuring distributional preferences in resource allocation tasks as well as proper games. Specifically we examine choice behavior in the contexts of role certainty, role uncertainty, decomposed games, and matrix games. Results show that there is large heterogeneity in the choices people make when deciding how to allocate resources between themselves and some other person under different contextual frames. For instance, people make more prosocial choices under role uncertainty as compared to role certainty. Furthermore, altering the way information is displayed given a particular situation can have a more dramatic effect on choice behavior than altering the situation itself. That is, depending on how information is displayed, people may behave as if they would perform a non-strategic decision making task when in fact they are playing a proper game characterized by strategic interdependence. Full article

We analyze choices of sellers, each setting a reserve price in a laboratory first price auction with automated equilibrium bidding. Subjects are allowed to gain experience for a fixed period of time prior to making a single payoff-relevant choice. Behavior of more experienced sellers was consistent with benchmark theory: average reserve price for these sellers was independent of the number of bidders and equaled the predicted level. Less experienced sellers however deviated from the theoretical benchmark: on average, they tended to shade reserve price below the predicted level and positively relate it to the number of bidders. Full article

Previous research has typically focused on distribution problems that emerge in the domain of gains. Only a few studies have distinguished between games played in the domain of gains from games in the domain of losses, even though, for example, prospect theory predicts differences between behavior in both domains. In this study, we experimentally analyze players’ behavior in dictator and ultimatum games when they need to divide a monetary loss and then compare this to behavior when players have to divide a monetary gain. We find that players treat gains and losses differently in that they are less generous in games over losses and react differently to prior experiences. Players in the dictator game become more selfish after they have had the experience of playing an ultimatum game first. Full article

We examine the impact of social distance in dictator game giving. The study is conducted in a field setting with high stakes (two days’ wages). The sample is a representative sample from eleven low-income Mexican villages. Subjects make multiple dictator decisions simultaneously, in a comparative dictator game. We show the relationship between social distance and giving using several family members, a member of the same village, and a stranger from a different village. Dictator giving shows substantial variation across recipient types and varies directly with social distance. We find higher giving towards family members than towards community members and strangers. Furthermore, our results indicate that giving to community members and to strangers is not different. In light of our results, it is important to consider the impact of social distance on inter- and intra-household transfers in policy interventions that alleviate poverty, e.g., conditional transfers. Full article

We consider a dominant platform provider operating both legacy and new platforms that connects users with suppliers in a two-sided market context. In addition to the typical indirect network effects in the two-sided market, backward compatibility works on the new platform. Thus, users joining the new one can also enjoy the services provided by suppliers using the legacy platform. Users and suppliers are linearly differentiated between two platforms as in the Hotelling model and play a subscription game of choosing one platform at the lower level. The suppliers in the new platform may suffer from congestion, which can be alleviated by platform provider’s investment on the new one. The platform provider also determines price margins for the supplier sides. Our equilibrium (eq.) analysis in the subscription game identifies an interior eq. (coexistence of both platforms in both sides). Though the backward compatibility plays a stabilizing role for the interior eq., its stability is fragile due to the network effects. Rather, some boundary eq.’s, where at least one side tips to the legacy or the new platform, are more likely to be stable. The backward compatibility is a key factor that characterizes the stable boundary eq.’s. The upper stage game is led by the platform provider, which tries to maneuver the system toward one of the stable boundary eq.’s using price margins and investment. The platform provider prefers an all-new boundary eq. when the indirect network effect and the maximum price margin for the new platform are large; thus, it puts a significant investment in the new one. With a small indirect network effect for suppliers, however, the platform provider does not invest in the new platform and choose a separate boundary eq. where two sides split into different platforms. Whether the user side completely tips to the new one (completely separated eq.) or not (partially separated eq.) depends on the backward compatibility. The relative advantage of the all-new eq. over the separate eq.’s in terms of social welfare from both sides depends on the backward compatibility as well as the indirect network effects for the new platform. Full article

A number of studies discuss whether and how economists differ from other disciplines in the amount that they contribute to public goods. We view this debate as incomplete because it neglects the willingness to sanction non-cooperative behavior, which is crucial for maintaining social order and for sustaining the provision of public goods. We study the decision whether to engage in costly punishment of a free rider in a survey-based experiment with 1423 students from seven study areas in the social sciences, as well as medicine at Aarhus University, Denmark. Using a dictator game and a social dilemma game, that captures essential features of the public goods game, we replicate previous findings that economics students give significantly less than students from other disciplines. However, when subjects decide whether or not to punish a free rider, we find that economics students are just as likely to punish as students from other disciplines. Full article

Social preference models emphasize that perceived intentions motivate reciprocity. However, laboratory tests of this theory typically manipulate perceived intentions through changes in wealth resulting from a sacrifice in pay by another. There is little evidence on whether reciprocity occurs in response to perceived intentions alone, independent of concurrent changes in pay and giver sacrifice (and any associated guilt from that sacrifice). This paper addresses this gap in the literature by implementing a modified dictator game where gifts to dictators are possible, but where gift transactions are also stochastically prevented by nature. This leads to instances of observed gift-giving intentions that yield no sacrifice or change in outcomes. In addition, this study uses both monetary and non-monetary gifts; previous studies typically use only monetary incentives, even though real-world applications of this literature often involve non-monetary incentives such as business or marketing gifts. The results show that on average, dictators reciprocated strongly to just the intention to give a gift, and they also reciprocated similarly to both monetary and non-monetary gifts. These results are consistent with intentions-based models of social preferences and with much of the marketing literature on business gifts. Full article