Failure in International Cooperation in the Presence of a Third Party

One of the most notable achievements of game theory is the theoretic result called “Folk Theorem”. This theorem states that players who cannot achieve cooperative outcomes in a one-period (or short-term) relationship can succeed in making cooperation available to themselves in the repeated game of a stage game sufficiently many times and they are not severely myopic. Unfortunately, there are many observations in reality in which a longer-term relationship cannot produce cooperation among the parties who are placed in a repeated game situation and attach proper importance to the future. This paper presents a realistic explanation in a game theoretic framework to show how this can the case. The idea rests on the presence of a third party. Cooperative outcomes that could be obtained in the the repeated game between the two players in the absence of a third party can be obstructed by the externality emitted from a third party. Consider two players, and , who play a repeated game repeating a stage game in which pure strategy Nash equilibrium. is Pareto inefficient. Suppose that there is a third player, namely , who is engaged in repeated game with and . Suppose also that cooperation is not achieved between and J on account of 's myopia. Both and struves to find a way to achieve the cooperative outcome that makes both of them better off. If by any chance has the influence on , which is reflected in the games in the way that can affect the payoff structure of both the games that is engaged in. To be specific, 's stance toward Q affects the payoffs of the two normal-form games that is engaged in, one with and the other with . It can be in the interest of that it makes a strategic use of in order to achieve cooperation with . That is, this strategic influecne of on can benefit if (i) the gain to is greater than the loss to and; (ii) and make an arrangement that will induce to take a strategic advantag of . In this scenario, the cooperation between and which is achieved is thwarted by the presence of a third party. Rather, the cooperation between and which is not achieved if does not take a strategic use of is obtained when comes to have an incentive to treat and ruin its cooperation with by the strategic stance toward . This paper clearly shows that it might be hasty to conclude that adequately forward-looking players can reach an cooperative outcome. This paper helps understand a real-world relationship between Korea, Japan and USA in support of its theoretic finding.