Consensus towards Partially Cooperative Strategies in Self-Regulated Evolutionary Games on Networks

Cooperation is widely recognized to be fundamental for the well-balanced development of human societies. Several different approaches have been proposed to explain the emergence of cooperation in populations of individuals playing the Prisoner’s Dilemma game, characterized by two concurrent natural mechanisms: the temptation to defect and the fear to be betrayed by others. Few results are available for analyzing situations where only the temptation to defect (Chicken game) or the fear to be betrayed (Stag-Hunt game) is present. In this paper, we analyze the emergence of full and partial cooperation for these classes of games. We find the conditions for which these Nash equilibria are asymptotically stable, and we show that the partial one is also globally stable. Furthermore, in the Chicken and Stag-Hunt games, partial cooperation has been found to be more rewarding than the full one of the Prisoner’s Dilemma game. This result highlights the importance of such games for understanding and sustaining different levels of cooperation in social networks.

Adaptations for Sharing Honest and Dishonest Gossip: A Fitness Interdependence Analysis

Gossip, which involves sharing information about absent others, has been identified as an effective solution to free rider problems in situations with conflicting interests between self and others. Yet, the information transmitted via gossip can be biased, because gossipers may send dishonest information about others for personal gains. Such dishonest gossip makes reputation-based cooperation more difficult to evolve. In which situations are people likely to share honest or dishonest gossip? In this theoretical review, we use formal models to provide the theoretical foundation for individuals’ gossip strategies in situations where the gossiper has varying levels of fitness interdependence with the target and/or the recipient. Our models across four different games (i.e., stag-hunt game, snowdrift game, helping game, and punishment game) illustrate that the gossiper’s action will be determined by (a) the gossiper’s fitness interdependence with the recipient and the target, and (b) the marginal cost/benefit in terms of payoff differences between two possible game actions for the recipient and the target (i.e., game type). Our models suggest a simple rule that gossipers can use to make optimal decisions even under noise. We discuss empirical examples that support the predictions of our model and potential extensions.

Collaboration and Gender Focality in Stag Hunt Bargaining

Knowing the gender of a counterpart can be focal in the willingness to collaborate in team settings that resemble the classic coordination problem. This paper explores whether knowing a co-worker’s gender affects coordination on the mutually beneficial outcome in a socially risky environment. In an experimental setting, subjects play a one-shot stag hunt game framed as a collaborative task in which they can “work together” or “work alone.” We exogenously vary whether workers know the gender of their counterparts pre-play. When gender is revealed, female players tend to gravitate to collaboration and efficient coordination regardless of the knowledge. Males, when knowingly paired with another male, tend to collaborate less, and thus, are less likely to coordinate on the Pareto optimal outcome. These results demonstrate one way that gender focality can lead to inefficient outcomes and provide insight for organizations looking to induce collaboration among workers.

The differential impact of friendship on cooperative and competitive coordination

Friendship is commonly assumed to reduce strategic uncertainty and enhance tacit coordination. However, this assumption has never been tested across two opposite poles of coordination involving either strategic complementarity or substitutability. We had participants interact with friends or strangers in two classic coordination games: the stag-hunt game, which exhibits strategic complementarity and may foster “cooperation”, and the entry game, which exhibits strategic substitutability and may foster “competition”. Both games capture a frequent trade-off between a potentially high paying but uncertain option and a low paying but safe alternative. We find that, relative to strangers, friends are more likely to choose options involving uncertainty in stag-hunt games, but the opposite is true in entry games. Furthermore, in stag-hunt games, friends “tremble” less between options, coordinate better and earn more, but these advantages are largely decreased or lost in entry games. We further investigate how these effects are modulated by risk attitudes, friendship qualities, and interpersonal similarities.

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.

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.