Stag Hunt Game Research Articles

A win-switch-lose-stay strategy promotes cooperation in the evolutionary games

The subject of how and why cooperation emerges in real world has been intensively investigated. A number of mechanisms have been found to favor cooperation in ecological systems and human societies. Here, we propose a win-switch-lose-stay strategy whose core lies in two aspects: (i) An individual, according to Fermi updating rule, first selects one neighbor stochastically from all its nearest neighbors to play the game to update its strategy of the first round, and memories the selected neighbor. (ii) The individual interacts with the selected neighbor in the last round if its accumulated payoff is lower than that of the selected neighbor, otherwise the selected neighbor randomly switches to another of its rest neighbors. Other individuals also follow the updating rule and repeat this evolutionary process. Simulation results reveal that the proposed strategy can remarkably promote cooperation in several social dilemmas, including the prisoner’s dilemma, the snowdrift game and the stag-hunt game.

Combining niche and game theories to address interspecific cooperation in ecological communities

Incorporating cooperative interspecific interactions into the classical Niche Theory has been identified as a big challenge of population and community ecology. Attempting to fill this gap I present the Lotka-Volterra Niche Game Model (LVNGM), resulting from the marriage between the classical Niche Theory and Game Theory. I use this new framework to analyze the effects of including cooperative interspecific interactions on two global properties of a community, its aggregate biomass or total yield and its biodiversity, measured by the Shannon equitability. I consider different dilemma games, games for which neither pure competition nor pure cooperation are dominant/optimal strategies, which are popular in biology: the Prisoner's Dilemma (PD), the Snowdrift (SD) and the Stag-Hunt (SH) games. The main result is that these games lead to a higher total yield—which is maximum for the SD, followed by the PD and the SH in third place—and, generally, to a higher biodiversity than pure competition. LVNGM allows gaining insights into niche construction/engineering. Examples in which LVNGM can be applied range from several single-trophic natural communities, in which positive interactions have been detected, to overyielding of artificial polycultures and plant-pollinator networks.

Preferences for efficiency, rather than preferences for morality, drive cooperation in the one-shot Stag-Hunt game

Recent work highlights that cooperation in the one-shot Prisoner's dilemma (PD) is primarily driven by moral preferences for doing the right thing, rather than social preferences for equity or efficiency. To our knowledge, nothing is known on whether moral preferences affect cooperation in the Stag-Hunt Game (SHG). Cooperation in the SHG fundamentally differs from cooperation in the PD in that it is not costly, but risky: players have no temptation to deviate from the cooperative outcome, but cooperation only pays off if the other player cooperates. Here we provide data from two experiments (total N = 523) to investigate SHG cooperation. Contrary to what has been observed for the PD, we find that SHG cooperation is primarily driven by preferences for efficiency, rather than moral preferences for doing the right thing.

Do Smartphones Create a Coordination Problem for Face-to-Face Interaction? Leveraging Game Theory to Understand and Solve the Smartphone Dilemma.

Smartphone use changes the landscape of social interactions, including introducing new social dilemmas to daily life. The challenge of putting down one's smartphone is an example of a classic coordination problem from game theory: the stag hunt game. In a stag hunt game, there are two possible coordination points, one that involves big payoffs for both partners (e.g., working together to hunt large game like stag) and one that involves smaller payoffs for both partners (e.g., individually hunting small game like rabbits) but is safer because it does not require that your partner choose that option as well. This is similar to the challenges of putting down smartphones to have a face-to-face interaction: you and your interaction partner might both prefer the higher payoff option of having a face-to-face interaction, but neither of you wants to put down your phone and risk not having anything to do in the meantime. It is also discussed how new technological innovations are changing the payoffs of face-to-face conversation versus side-by-side smartphone scrolling. Insights that come from applying game theory to this "social media dilemma" are discussed here and potential solutions that come out of a game theoretic analysis are offered. Also see the video abstract here https://youtu.be/9esL578zM-E.

Games as frames

We show that economic games per se can provide contextual cues and thereby impact behavior. In two laboratory experiments, we examine whether deliberating on trust games versus stag-hunt games without feedback changes cooperation behavior in a subsequent game. First, we find that subjects who play trust games without feedback hold more pessimistic beliefs about other players’ cooperation in a subsequent game than subjects who played stag-hunt games without feedback. We also observe that deliberation on trust games versus stag-hunt games accordingly affects behavior in a subsequent, unrelated game. While stag-hunt games align interests between players, trust games pose a conflict of interest between players. Such (mis-)alignments induced by the game potentially explain our findings, because they may offer cues that affect beliefs and behavior in subsequent games.

Ranking the invasions of cheaters in structured populations

The identification of the most influential individuals in structured populations is an important research question, with many applications across the social and natural sciences. Here, we study this problem in evolutionary populations on static networks, where invading cheaters can lead to the collapse of cooperation. We propose six strategies to rank the invading cheaters and identify those which mostly facilitate the collapse of cooperation. We demonstrate that the type of successful rankings depend on the selection strength, the underlying game, and the network structure. We show that random ranking has generally little ability to successfully identify invading cheaters, especially for the stag-hunt game in scale-free networks and when the selection strength is strong. The ranking based on degree can successfully identify the most influential invaders when the selection strength is weak, while more structured rankings perform better at strong selection. Scale-free networks and strong selection are generally detrimental to the performance of the random ranking, but they are beneficial for the performance of structured rankings. Our research reveals how to identify the most influential invaders using statistical measures in structured communities, and it demonstrates how their success depends on population structure, selection strength, and on the underlying game dynamics.

The Determinants of Efficient Behavior in Coordination Games

We study the determinants of efficient behavior in stag hunt games (2x2 symmetric coordination games with Pareto ranked equilibria) using both data from eight previous experiments on stag hunt games and data from a new experiment which allows for a more systematic variation of parameters. In line with the previous experimental literature, we find that subjects do not necessarily play the efficient action (stag). While the rate of stag is greater when stag is risk dominant, we find that the equilibrium selection criterion of risk dominance is neither a necessary nor sufficient condition for a majority of subjects to choose the efficient action. We do find that an increase in the size of the basin of attraction of stag results in an increase in efficient behavior. We show that the results are robust to controlling for risk preferences.

Berge Solution Concepts in the Graph Model for Conflict Resolution

In this work, we generalize Berge solution concepts in the graph model for conflict resolution for conflicts with 2 or more decision makers (DMs). These concepts are useful to the analysis of interactions among DMs with altruistic behaviors. Berge behavior can be observed in conflicts where DMs act altruistically expecting others to reciprocate so that in the end it is in their own self-interests to behave in this way. The Berge stabilities presented are inspired on commonly used stability notions in the GMCR, such as: generalized metarationality, symmetric metarationality, sequential and symmetric sequential stabilities for conflicts with 2 or more DMs. We investigate the relation among these proposed concepts and also between such concepts and the standard ones. We also establish a relationship between Berge stability and coalition Nash stability of a modified conflict. The chicken and stag hunt games are used as examples to illustrate applications of the Berge stabilities in conflicts. In particular, we show that in the stag hunt game and in a modified version of it, Berge stabilities may be used to select a more desired Nash equilibria.

A single 'weight-lifting' game covers all kinds of games.

Game theory has been studied extensively to answer why cooperation is promoted in human and animal societies. All games are classified into five games: the Prisoner's Dilemma, chicken game (including hawk–dove game), stag hunt game and two trivial games of either all cooperation or all defect, which are studied separately. Here, we propose a new game that covers all five game categories: the weight-lifting game. The player choose either to (1) carry a weight (cooperate: pay a cost) or (2) pretend to carry it (defect: pay no cost). The probability of success in carrying the weight depends on the number of cooperators, and the players either gain the success reward or pay the failure penalty. All five game categories appear in this game depending on the success probabilities for the number of cooperators. We prove that this game is exactly equivalent to the combination of all five games in terms of a pay-off matrix. This game thus provides a unified framework for studying all five types of games.

Coordination Games in Continuous Time

This paper studies the impact of continuous time interaction on two iconic coordination games: stag hunt and battle of the sexes in a laboratory environment and compare results to possible theoretical explanations. Experimental results show that subjects consistently coordinate better in continuous time than in discrete time under various treatment environments. In continuous time, they are also more likely to converge to payoff-dominant equilibrium in stag hunt games and alternating dynamics in battle of the sexes games. Furthermore, the coordination rate is affected by complexity of action sets and weakly influenced by payoff matrices. The paper also explores some stylized facts that result in the treatment effects.

Intuition and Deliberation in the Stag Hunt Game

We present an incentivized laboratory experiment where a random sample of individuals playing a series of stag hunt games are forced to make their choices under time constraints, while the rest of the players have no time limits to decide. We find that individuals under the time pressure treatment are more likely to play stag (vs. hare) than individuals in the control group: under time constraints 62.85% of players are stag-hunters as opposed to 52.32% when no time limits are imposed. These results offer the first experimental evidence on the role of intuition and deliberation in strategic situations that entail social coordination. In interpreting our findings, we provide a discussion on ruling social conventions in daily-life interactions.

Memory mechanism with weighting promotes cooperation in the evolutionary games

Abstract Memory normally plays an important role when investigating the collective behaviours in real world. Each rational player can get a more reasonable strategy by comprehensively considering certain amount of historical information within its memory scope. Motivated by the fact, we here propose a memory mechanism with weighting whose core lies in three aspects: (i) Each player applies a memory rule to compare its own historical accumulated payoffs inside the range of memory length and to take the maximal one and corresponding strategy as historical optimal accumulated payoff and historical optimal strategy; (ii) Each neighbour of a player is endowed with a weighting which is the ratio of historical optimal accumulated payoff of each neighbour to the total historical optimal accumulated payoff of all neighbours of the player; (iii) Each player interacts with a neighbour selected by probability equal to weighting, and then updates its historical optimal strategy according to Fermi function. The asynchronous updating algorithm is used to study the evolution of cooperation with different memory lengths on a regular lattice. Simulation results show that the proposed mechanism effectively promotes cooperation in three classical social dilemmas. Moreover, it is revealed that the cooperation level, by and large, increases first and then decreases as the memory length increases in the prisoner’s dilemma and snowdrift game, and that the cooperation level increases as so does the memory length in the stag-hunt game.

The evolution of conventions under condition-dependent mistakes

We study the long-run conventions emerging in a stag-hunt game when agents are myopic best responders. Our main novel assumption is that errors converge to zero at a rate that is positively related to the payoff earned in the past. To fully explore the implications of this error model, we introduce a further novelty in the way we model the interaction structure, assuming that with positive probability agents remain matched together in the next period. We find that, if interactions are sufficiently persistent over time, then the payoff-dominant convention emerges in the long run, while if interactions are quite volatile, then the maximin convention can emerge even if it is not risk-dominant. We contrast these results with those obtained under two alternative error models: uniform mistakes and payoff-dependent mistakes.

Preferences for Efficiency, Rather Than Preferences for Morality, Drive Cooperation in the One-Shot Stag-Hunt Game

Recent work highlights that cooperation in the one-shot Prisoner’s dilemma (PD) is primarily driven by moral preferences for doing the right thing, rather than social preferences for equity or efficiency. By contrast, little is known on what motivates cooperation in the Stag-Hunt Game (SHG). Cooperation in the SHG fundamentally differs from cooperation in the PD in that it is not costly, but risky: players have no temptation to deviate from the cooperative outcome, but cooperation only pays off if the other player cooperates. Here, we provide data from a large (N=436), pre-registered, experiment. Contrary to what has been observed for the PD, we find that SHG cooperation is primarily driven by preferences for efficiency, rather than preferences for doing the right thing.

Stag hunt as an analogy for systems-of-systems engineering

Systems-of-systems engineering deals with a special class of engineered systems that lack the central control common in traditional systems engineering problems. This paper introduces the stag hunt game as an analogy for the fundamental collective decision-making challenges in systems-of-systems engineering. The stag hunt models a dilemma between two viable alternatives: an independent strategy that minimizes risk and a collaborative strategy that maximizes payoff. Results of equilibrium selection theory provide insights to ensure collaboration in systems-of-systems including maximizing upside potential, minimizing downside risk, and mitigating systemic risk sources such as cost overruns.

Memory-based stag hunt game on regular lattices

Memory normally plays an important role when people make a decision. Thus, it is reasonable and necessary to introduce the influence of memory in the evolutionary game theory. However, the previous work mainly focuses on prisoner’s dilemma, snowdrift game or public good game, but little on stag hunt game. In this paper, a memory-based stag hunt game is proposed. For each iteration, the players in the regular lattices will first choose its neighbor who has the largest accumulated payoff in the last M runs. Then, according to the Femi rule, the player will determine whether learning from the neighbor or not. It is found that the memory length M will promote the cooperation level. The larger the memory length is, the higher the cooperation level will be. Furthermore, when the payoff parameter is less than 0.75, cooperation will always spread the whole regular lattices. As the parameter is larger than 0.75, no matter how large the memory length is, the behavior of defection will always exist. Our work may shed some new light on the study of evolutionary games with memory effect.

Cooperation percolation in spatial evolutionary games

It has been known that the formation of cooperator clusters plays an important role in spatial evolutionary games. By gathering together, cooperators assist each other and the benefits of mutual cooperation can outweigh the losses against the defector. In this letter, we study the dynamical organization of cooperator clusters in the spatial Stag Hunt game, the Prisoner's Dilemma game and the Snowdrift game. For the above games in square lattices, there exists a continuous phase transition characterized by the emergence of a large spanning cooperator cluster which occurs when the initial fraction of the cooperators exceeds a certain threshold. For games in random graphs, there exist two different kinds of phase transitions. At the first the normalized size of the giant cooperator cluster increases continuously from zero, and at the second the normalized size of the giant cooperator cluster jumps from a low value to a very high value.

Memory-based conformity enhances cooperation in social dilemmas

The problem of how cooperative behaviors emerge in real world has been widely investigated and it is found that cooperative behaviors are closely related to memory, which means a rational player can get a more reasonable strategy by comprehensively considering certain amount of historical information within its memory scope. On the other hand, due to the potential risk during pursuing high payoff in human society, selecting the most common strategy for a player inside the interaction range is relatively safer, at least its payoff is not much lower than average, which is known as conformity. Motivated by these facts, we here propose a mechanism of conformity with memory whose core lies in two facts: (i) Each player first applies a memory rule to compare its own historical payoffs with a limited memory length and to take the strategy corresponding to the maximal payoff as historical optimal strategy; (ii) Each player can get the virtual optimal strategy by selecting the most common strategy from its neighbors’ historical optimal strategies according to the conformity rule. The asynchronous updating algorithm, together with the virtual strategy, is used to study the evolution of cooperation with different memory lengths on a regular lattice. Simulation results show that the proposed mechanism remarkably promotes cooperation in three classical evolutionary social dilemmas. More specifically, it is revealed that the cooperation level decreases gradually as the memory length increases in the prisoner’s dilemma and snowdrift game, and that the cooperation level increases as so does the memory length in the stag-hunt game.

BEHAVIOR REACTIONS CHARACTERISTIC OF THE INDIVIDUALS WITH EGOISTIC AND ALTRUISTIC TYPE OF SOCIAL BEHAVIOR

Different types of social behavior are characterized by different behavioral reactions. Characteristics of selfish and altruistic social behavior are not clearly confirmed by the data of psychophysiological studies. Therefore, the purpose of the work is to identify the peculiarities of behavioral reactions of individuals with more expressed egoistic and altruistic social behavior, which are based on data of electroencephalographic research. 120 (aged 21±4 years) individuals took part in the study. As a result of complex psychological testing (based on Leary’s test) all subjects were divided into two groups - altruistic and egoistic. Registration of electrical activity was carried out in a model of collective interaction using the Stag Hunt Game and a specially developed model of social behavior Mini-Basketball. The number of elections for egoistic and altruistic stimulus and the reaction time to them were observed in the study. The stimulus "Rabbit" and "Throw" were considered as egoistic; “Stag" and "Pass" - as altruistic in accordance with the test methods. As a result, the frequency of choosing the type of stimuli corresponds to the social orientation of the individuals. The reaction time increases with the choice of the type of stimulus, which does not coincide with the type of social orientation of the subject.

Self-Organizing Cooperative Dynamics in Government Extended Enterprises

This paper presents the results of our research into cooperation in Government Extended Enterprises, a type of system of systems. The effort proposed and evaluated a novel theory that these decisions are the result of the interaction of four canonical forces—Sympathy, Trust, Fear, and Greed. A computational simulation involving the Stag Hunt game examined information sharing decisions in a series of key decision points in three large case studies. For the five hypotheses tested, exploratory data analysis and nonparametric statistical testing show strong support for three of the hypotheses (cooperation is positively correlated with actors’ levels of Sympathy and Trust and negatively correlated with actors’ levels of Fear) and moderate support for the fourth (cooperation is negatively correlated with actors’ levels of Greed). Indications are that the fifth hypothesis (cooperation is correlated with history of behavior) is not needed to explain observed behavior. Multiple correspondence analysis showed significant interactions both among pairs of forces and when a force is paired with decision making strategies. These results can form the basis for: 1) analysis of additional case studies; 2) development of an agent-based simulation; and 3) creation of training programs for current and future organizational leaders.