Games, Volume 10, Issue 1 (March 2019) – 15 articles

There is a large body of evidence showing that a substantial proportion of people cooperate in public goods games, even if the situation is one-shot and completely anonymous. In the present study, we bring together two major endogenous factors that are known to affect cooperation levels, and in so doing replicate and extend previous empirical research on public goods problems in several important ways. We measure social preferences and concurrently elicit beliefs on the individual level using multiple methods, and at multiple times during the experiment. With this rich set of predictor variables at the individual level, we test how well individual contribution decisions can be accounted for in both a one-shot and a repeated interaction. We show that when heterogeneity in people’s preferences and beliefs is taken into consideration, more than 50% of the variance in individual choice behavior can be explained. Furthermore, we show that people do not only update their beliefs in a repeated public goods game, but also that their social preferences change, to some extent, in response to the choices of other decision makers. Full article

Agency may be exercised by different entities (e.g., individuals, firms, households). A given individual can form part of multiple agents (e.g., he may belong to a firm and a household). The set of agents that act in a given situation might not be common knowledge. We adapt the standard model of incomplete information to model such situations. Full article

For cancer, we develop a 2-D agent-based continuous-space game-theoretical model that considers cancer cells’ proximity to a blood vessel. Based on castrate resistant metastatic prostate cancer (mCRPC), the model considers the density and frequency (eco-evolutionary) dynamics of three cancer cell types: those that require exogenous testosterone ( $T^{+}$ ), those producing testosterone ( $T^P$ ), and those independent of testosterone ( $T^{-}$ ). We model proximity to a blood vessel by imagining four zones around the vessel. Zone 0 is the blood vessel. As rings, zones 1–3 are successively farther from the blood vessel and have successively lower carrying capacities. Zone 4 represents the space too far from the blood vessel and too poor in nutrients for cancer cell proliferation. Within the other three zones that are closer to the blood vessel, the cells’ proliferation probabilities are determined by zone-specific payoff matrices. We analyzed how zone width, dispersal, interactions across zone boundaries, and blood vessel dynamics influence the eco-evolutionary dynamics of cell types within zones and across the entire cancer cell population. At equilibrium, zone 3’s composition deviates from its evolutionary stable strategy (ESS) towards that of zone 2. Zone 2 sees deviations from its ESS because of dispersal from zones 1 and 3; however, its composition begins to resemble zone 1’s more so than zone 3’s. Frequency-dependent interactions between cells across zone boundaries have little effect on zone 2’s and zone 3’s composition but have decisive effects on zone 1. The composition of zone 1 diverges dramatically from both its own ESS, but also that of zone 2. That is because $T^{+}$ cells (highest frequency in zone 1) benefit from interacting with $T^P$ cells (highest frequency in zone 2). Zone 1 $T^{+}$ cells interacting with cells in zone 2 experience a higher likelihood of encountering a $T^P$ cell than when restricted to their own zone. As expected, increasing the width of zones decreases these impacts of cross-boundary dispersal and interactions. Increasing zone widths increases the persistence likelihood of the cancer subpopulation in the face of blood vessel dynamics, where the vessel may die or become occluded resulting in the “birth” of another blood vessel elsewhere in the space. With small zone widths, the cancer cell subpopulations cannot persist. With large zone widths, blood vessel dynamics create cancer cell subpopulations that resemble the ESS of zone 3 as the larger area of zone 3 and its contribution to cells within the necrotic zone 4 mean that zones 3 and 4 provide the likeliest colonizers for the new blood vessel. In conclusion, our model provides an alternative modeling approach for considering density-dependent, frequency-dependent, and dispersal dynamics into cancer models with spatial gradients around blood vessels. Additionally, our model can consider the occurrence of circulating tumor cells (cells that disperse into the blood vessel from zone 1) and the presence of live cancer cells within the necrotic regions of a tumor. Full article

Previous research on cooperation has primarily focused on egalitarian interactions, overlooking a fundamental feature of social life: hierarchy and power asymmetry. While recent accounts posit that hierarchies can reduce within-group conflict, individuals who possess high rank or power tend to show less cooperation. How, then, is cooperation achieved within groups that contain power asymmetries? To address this question, the present research examines how relative power affects cooperation and strategies, such as punishment and gossip, to promote cooperation in social dilemmas. In two studies involving online real-time interactions in dyads (N = 246) and four-person groups (N = 371), we manipulate power by varying individuals’ ability to distribute resources in a dictator game, and measure punishment, gossip, and cooperative behaviors in a multi-round public goods game. Findings largely replicate previous research showing that punishment and gossip opportunities increase contributions to public goods in four-person groups. However, we find no support for the hypotheses that power directly affects cooperation or the use of punishment and gossip to promote cooperation. We discuss the implications of these findings for understanding the influence of hierarchy and power on cooperation within dyads and groups. Full article

Social dilemmas are among the most puzzling issues in the biological and social sciences. Extensive theoretical efforts have been made in various realms such as economics, biology, mathematics, and even physics to figure out solution mechanisms to the dilemma in recent decades. Although punishment is thought to be a key mechanism, evolutionary game theory has revealed that the simplest form of punishment called peer punishment is useless to solve the dilemma, since peer punishment itself is costly. In the literature, more complex types of punishment, such as pool punishment or institutional punishment, have been exploited as effective mechanisms. So far, mechanisms that enable peer punishment to function as a solution to the social dilemma remain unclear. In this paper, we propose a theoretical way for peer punishment to work as a solution mechanism for the dilemma by incorporating prospect theory into evolutionary game theory. Prospect theory models human beings as agents that estimate small probabilities and loss of profit as greater than they actually are; thus, those agents feel that punishments are more frequent and harsher than they really are. We show that this kind of cognitive distortion makes players decide to cooperate to avoid being punished and that the cooperative state achieved by this mechanism is globally stable as well as evolutionarily stable in a wide range of parameter values. Full article

Since social dilemmas among n-persons are often embedded in other types of social exchanges, the exclusion of defectors in social dilemmas from other exchanges functions as a costless selective incentive. Recently, such “linkage” has been considered as a promising solution to resolve the social dilemma problem. However, previous research showed that cooperation sustained by linkage is fragile when subjective perception errors exist. The purpose of this study is to find linkage strategies that are robust against subjective perception errors. Based on the strategies presented in previous studies on indirect reciprocity, we devised several linkage strategies and examined their evolutionary stability by agent-based simulation. The simulation results showed that the linkage strategy based on kandori was evolutionarily stable even when perception errors existed. Our study provides substantial support for the argument that linkage is a plausible solution to the social dilemma problem. Full article

In this paper we present a novel experimental procedure aimed at better understanding the interaction between confidence and ambiguity attitudes in individual decision making. Different ambiguity settings not only can be determined by the lack of information in possible scenarios completely “external” to the decision-maker, but can also be a consequence of the decision maker’s ignorance about her own characteristics or performance and, thus, deals with confidence. We design a multistage experiment where subjects face different sources of ambiguity and where we are able to control for self-assessed levels of competence. By means of a Principal Component Analysis, we obtain a set of measures of “internal” and “external” ambiguity aversion. Our regressions show that the two measures are significantly correlated at the subject level, that the subjects’ “internal” ambiguity aversion increases in performance in the high-competence task and that “external” ambiguity aversion moderately increases in earnings. Self-selection does not play any role. Full article

This paper studies a two-person trading game in continuous time that generalizes Garivaltis (2018) to allow for stock prices that both jump and diffuse. Analogous to Bell and Cover (1988) in discrete time, the players start by choosing fair randomizations of the initial dollar, by exchanging it for a random wealth whose mean is at most 1. Each player then deposits the resulting capital into some continuously rebalanced portfolio that must be adhered to over $[0,t]$ . We solve the corresponding “investment $\varphi$ -game”, namely the zero-sum game with payoff kernel $\mathbb{E}\left[\varphi \{{\mathbf{W}}_1{V}_t\left(b\right)/\left({\mathbf{W}}_2{V}_t\left(c\right)\right)\}\right]$ , where ${\mathbf{W}}_i$ is player i’s fair randomization, $V_t\left(b\right)$ is the final wealth that accrues to a one dollar deposit into the rebalancing rule b, and $\varphi (•)$ is any increasing function meant to measure relative performance. We show that the unique saddle point is for both players to use the (leveraged) Kelly rule for jump diffusions, which is ordinarily defined by maximizing the asymptotic almost-sure continuously compounded capital growth rate. Thus, the Kelly rule for jump diffusions is the correct behavior for practically anybody who wants to outperform other traders (on any time frame) with respect to practically any measure of relative performance. Full article

The problem of the existence of Berge equilibria in the sense of Zhukovskii in normal-form finite games in pure and in mixed strategies is studied. The example of a three-player game that has Berge equilibrium neither in pure, nor in mixed strategies is given. Full article

I study the path properties of adaptive heuristics that mimic the natural dynamics of play in a game and converge to the set of correlated equilibria. Despite their apparent differences, I show that these heuristics have an abstract representation as a sequence of probability distributions that satisfy a number of common properties. These properties arise due to the topological structure of the set of correlated equilibria. The characterizations that I obtain have useful applications in the study of the convergence of the heuristics. Full article

We study a model where agents face a continuum of two-player games and categorize them into a finite number of situations to make sense of their complex environment. Agents need not share the same categorization. Each agent can cooperate or defect, conditional on the perceived category. The games are fully ordered by the strength of the temptation to defect and break joint cooperation. In equilibrium agents share the same categorization, but achieve less cooperation than if they could perfectly discriminate games. All the equilibria are evolutionarily stable, but stochastic stability selects against cooperation. We model agents’ learning when they imitate successful players over similar games, but lack any information about the opponents’ categorizations. We show that imitation conditional on reaching an intermediate aspiration level leads to a shared categorization that achieves higher cooperation than under perfect discrimination. Full article

Mutation-generated variation in behavior is thought to promote the evolution of cooperation. Here, we study this by distinguishing two effects of mutation in evolutionary games of the finitely repeated Prisoner’s Dilemma in infinite asexual populations. First, we show how cooperation can evolve through the direct effect of mutation, i.e., the fitness impact that individuals experience from interactions with mutants before selection acts upon these mutants. Whereas this direct effect suffices to explain earlier findings, we question its generality because mutational variation usually generates the highest direct fitness impact on unconditional defectors (AllD). We identify special conditions (e.g., intermediate mutation rates) for which cooperation can be favored by an indirect effect of mutation, i.e., the fitness impact that individuals experience from interactions with descendants of mutants. Simulations confirm that AllD-dominated populations can be invaded by cooperative strategies despite the positive direct effect of mutation on AllD. Thus, here the indirect effect of mutation drives the evolution of cooperation. The higher level of cooperation, however, is not achieved by individuals triggering reciprocity (‘genuine cooperation’), but by individuals exploiting the willingness of others to cooperate (‘exploitative cooperation’). Our distinction between direct and indirect effects of mutation provides a new perspective on how mutation-generated variation alters frequency-dependent selection. Full article

I investigate how different dispersal patterns affect the evolution of cooperation in a spatially-structured population. I consider a finite fixed-size population of cooperators and free-riders residing on a one-dimensional lattice with periodic boundaries. Individuals interact via a multiplayer game, which is a version of a public goods game, and the population evolves via a Moran process. Individuals try to improve their interactions by evaluating the current state of the environment and moving to locations with better payoffs. I ran stochastic simulations of the evolution of this Markov process and found that if individuals disperse deterministically to locations with the best payoffs, then cooperation can still be maintained even in the worst-case scenarios, albeit at reduced levels compared to the better-case scenarios. This contrasts with an earlier investigation of probabilistic dispersal patterns, which resulted in the breakdown of cooperation in sparse populations with small interaction neighborhoods, a high mobility rate, and a large dispersal range. Full article

We study the evolution of cooperation in group interactions where players are randomly drawn from well-mixed populations of finite size to participate in a public goods game. However, due to the possibility of unforeseen circumstances, each player has a fixed probability of being unable to participate in the game, unlike previous models which assume voluntary participation. We first study how prescribed stochastic opting-out affects cooperation in finite populations, and then generalize for the limiting case of large populations. Because we use a pairwise comparison updating rule, our results apply to both genetic and behavioral evolution mechanisms. Moreover, in the model, cooperation is favored by natural selection over both neutral drift and defection if the return on investment exceeds a threshold value depending on the population size, the game size, and a player’s probability of opting-out. Our analysis further shows that, due to the stochastic nature of the opting-out in finite populations, the threshold of return on investment needed for natural selection to favor cooperation is actually greater than the one corresponding to compulsory games with the equal expected game size. We also use adaptive dynamics to study the co-evolution of cooperation and opting-out behavior. Indeed, given rare mutations minutely different from the resident population, an analysis based on adaptive dynamics suggests that over time the population will tend towards complete defection and non-participation, and subsequently cooperators abstaining from the public goods game will stand a chance to emerge by neutral drift, thereby paving the way for the rise of participating cooperators. Nevertheless, increasing the probability of non-participation decreases the rate at which the population tends towards defection when participating. Our work sheds light on understanding how stochastic opting-out emerges in the first place and on its role in the evolution of cooperation. Full article