We consider the repeated prisoner's dilemma (PD). We assume that players make their choices knowing only average payoffs from the previous stages. A player's strategy is a function from the convex hull S of the set of payoffs into the set {C, D} (C means cooperation, D-defection). Smale (Econometrica 48:1617-1634, 1980) presented an idea of good strategies in the repeated PD. If both players play good strategies then the average payoffs tend to the payoff corresponding to the profile (C, C) in PD. We adopt the Smale idea to define semi-cooperative strategies-players do not take as a referencing point the payoff corresponding to the profile (C, C), but they can take an arbitrary payoff belonging to the β-core of PD. We show that if both players choose the same point in the β-core then the strategy profile is an equilibrium in the repeated game. If the players choose different points in the β-core then the sequence of the average payoffs tends to a point in S. The obtained limit can be treated as a payoff in a new game. In this game, the set of players' actions is the set of points in S that corresponds to the β-core payoffs.
JEL classification C72, C73, D91Abstract : The paper examines an infinitely repeated 3-player extension of the Prisoner's Dilemma game. We consider a 3-player game in the normal form with incomplete information, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage, players make their choices knowing only the average payoffs from previous stages of all the players. A strategy of a player in the repeated game is a function defined on the convex hull of the set of payoffs. Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. a strategy profile being resistant to deviations by coalitions. Constructed equilibrium strategies are safe, i.e. the non-deviating player payoff is not smaller than the equilibrium payoff in the stage game, and deviating players' payoffs do not exceed the non-deviating player payoff more than by a positive constant which can be arbitrary small and chosen by the non-deviating player. Our construction is inspired by Smale's good strategies described in [17], where the repeated Prisoner's Dilemma was considered. In proofs we use arguments based on approachability and strong approachability type results.
Abstract. Based on the Bressan and Shen approach (Bressan and Shen, 2004;Shen, 2009), we present an extension of the class of non-zero sum differential games for which value functions are described by a weakly hyperbolic Hamilton-Jacobi system. The considered value functions are determined by a Pareto optimality condition for instantaneous gain functions, for which we compare two methods of the unique choice Pareto optimal strategies. We present the procedure of applying this approach for duopoly.
The rural areas of Castilla-La Mancha have managed to preserve a unique natural and cultural character. A great diversity of touristic qualities makes the region especially attractive for development of rural tourism.
For many years, the autonomous community of Castilla-La Mancha had to cope with numerous socio-economic difficulties. Development of the tourist industry resulted in diversification of income sources and higher level of employment. Another positive effect of the process was activation of female members of the community. The principle aim of this article is to underline the complementary role of tourism in rural areas in relation to agriculture and urban tourism.
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