Bargaining over Strategies of Non-Cooperative Games
The article provides insight to the bargaining process that integrates the process of non-corporative game theory. To understand the applicability of non-cooperative games, the authors discuss the uniqueness, the efficiency, and existence of the agreement reached in the bargaining process. The article shed light to the broad perspective of the non-cooperative games involving two players by including several games that involve the Ultimatum Game, the Prisoner's Dilemma, the Trust Game, the Hawk-Dove Game. Using these two-player non-cooperative games, the author found that the bargaining process proposed result in Pareto-efficient settlements, which typically differed from the Nash equilibrium obtained in the original games (Attanasi, García-Gallego, Georgantzís and Montesano, 2015).
The paper introduces the non-cooperative games of the two players by suggesting that in games such as Trust Game and Prisoner's Dilemma, the Nash equilibrium does not achive Pareto-efficient. According to the laboratory experiments, this contradicts the perception of human subjects who usually choose the strategy that achieves Pareto-efficient. In other words, people prefer strategies that make somebody better off by making another person worse off. However, the authors argue that this behavior is not rational in the perspective of theoretical game. Various studies indicate that individuals and societies apply socially desired deviations from the outcome of non-cooperative equilibrium (Attanasi et al. 2015, p.274). In the actual situations, people tend to bargain on their behaviors strategically.
The article defines confirmed proposal process as "a dynamic supergame that may or may not have a subgame perfect equilibrium" (Attanasi et al. 2015, p.296). Through this approach, the article found out that in cases where equilibrium prevails, the results of this process of bargaining is perceived as inadequately Pareto-efficient. The results may not always agree with the Nash equilibrium reached at the original game. In addition, when the original game becomes generic, the equilibrium illustrates that agreement is distinctive even in the situation where there is multiple Nash equilibrium. The player can choose to play the original game instead of bargaining over its strategy, especially when the payoff received is low than that obtained from the Nash equilibrium of the original game.
On the consequences of implementing the bargaining process, the paper theoretically found out that projected bargaining process produces Pareto-efficient bargains that differ from the obtained Nash equilibrium in the initial game. However, only in the Trust Game and Prisoner's Dilemma, the duo players can partake the bargaining process. In this case, the players are committed to playing the original game with accordance to the bargain suggested in the bargaining process. According to the Hawk-Dove Game, the players may not decide to bargain. The equilibrium suggests that bargains enables each player to have transitional payoff between the two Nash equilibria payoffs derived from unmodified game original game. The Ultimatum Game helps the player to reach on the unrestricted payoff. In this case, the player should not engage in the process of bargaining because he/she can obtain higher payoff when playing directly the original game. The paper concludes by suggesting that the results of the study apply to experiment can be perceived as rationalist elucidation of mental process individual utilize when they face social dilemmas such as the one explained in this article.
Attanasi, G., García-Gallego, A., Georgantzís, N., & Montesano, A. (2015). Bargaining over Strategies of Non-Cooperative Games. Games, 6(3), 273-298. doi:10.3390/g6030273