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Proceeding from the latest versions of the Folk theorems, this chapter shows that “natural” evolution of behavior in repeated games in human populations is a very unstable process which may be easily manipulated by outside forces. Any feasible and individually rational payoff of the game may be converted into a globally stable outcome by an arbitrary small perturbation of the payoff functions in the repeated game. We show that this result also holds for a trembling-hand perturbation of the game, and prove a new version of the Folk theorem for this case. This conclusion is in contrast to the result of R. Axelrod, K. Sigmund and M. A. Nowak and some other researches on the evolution of behavior in the repeated Prisoner’s Dilemma. We discuss the reasons for these different results.

In this chapter we consider a two-stage game with one leader and one (or more) followers and we investigate the behavior of a Tikhonov regularization when the best reply for the follower(s) is not uniquely determined. More precisely, we show, under mild assumptions in the case of one follower and sufficiently mild in the case of two followers, that a convergent sequence of solutions to regularized two-stage games generates a subgame perfect equilibrium (SPE) of the original game, providing a constructive way to approach an SPE in a continuous setting. Various elementary examples show that our results cannot be strengthened up to guaranteeing convergence to a strong or a weak Stackelberg equilibrium and that the method cannot be extended to all of the cases in which two followers play a mixed extension of a finite game.

The purpose of this chapter is twofold: (1) to bring a new concept of extended self in philosophy into the analysis of conflict resolution, and (2) to construct a game theoretic model with selves and extended selves as players which depicts a conflicting situation and to find its resolution. We find that extended selves could be a useful concept to unite players’ opposing ideas. We study a two-stage noncooperative game in which players are given by selves or extended selves and find that, for each player, to unite with another player is always a weakly dominant strategy when payoffs are symmetric and costs for unification are negligible.

Many models of energy market development and decision-making processes take into account the competition between energy suppliers, and the theory of games is an appropriate tool to study these problems.

This chapter is devoted to numerical analysis and modification of the game-theoretical gas market model developed by Klaassen, Kryazhimskii, and Tarasyev. We describe a software G-TIME elaborated for this purpose and the results of a simulation and sensitivity analysis on the data of the Turkish gas market. The last section deals with the notion of a generalized Nash equilibrium, which seems to be useful for taking risk and uncertainty into account. The research is based on approaches and methods developed in [–].

Here the dynamic fishery harvesting game is generalized to a stochastic environment in order to examine the implications of incomplete and asymmetric information. The main emphasis is on a split stream version of the game: At the beginning of each harvest season the initial fish stock (or “recruitment”) divides into two streams, each one accessible to harvest by just one of the two competing fishing fleets. The fleets simultaneously harvest down their streams, achieving net seasonal payoffs for the catch. After harvest, the residual sub-stocks reunite to form the broodstock for the subsequent generation. The strength of this subsequent generation is determined by a specified “stock-recruitment relation,” and the cycle repeats. In this cyclic process, both natural environmental factors (stream-split proportions and stock-recruitment relation) and economic factors (harvest costs and benefits) will incorporate Markovian stochastic elements. At the beginning of each season, both fleets know the current recruitment and also have some (generally incomplete or delayed, and often asymmetric) knowledge of the current values of the stochastic elements. The knowledge structure of each specific game version is held in common by the competitors. In the dynamic game each fleet sets its harvest policy with the objective of maximizing the expected discounted sum of seasonal payoffs, and conditional on the extent of its current knowledge and of the anticipated policy of its competitor.

The implications of alternative knowledge structures are explored, through dynamic programming and simulation. Both information structures and the stochastic characteristics of bioeconomic parameters are varied continuously to explore their interplay. The asymmetric trade-offs among them are examined. The focus is on demonstrating the often unex pected, and sometimes counter-intuitive, effects that knowledge enrichment may have in these incomplete-information, common-property games.

In this chapter we propose a dynamic game-theoretic modeling framework for the international climate change negotiations that should take place at the end of the Kyoto Protocol agreement if the necessity to drastically curb carbon emissions is confirmed. The model is composed of a set of optimal economic growth models corresponding to the different groups of nations that will be parties in the negotiations. Emissions of greenhouse gases (GHGs) are represented as by-products of the economic production process. Two types of capital (clean vs. dirty) can be used to produce the economic good with different emissions effects. The negotiations should determine a set of allowances that define caps on GHG emissions such that a long-term constraint on total emissions is satisfied. At each instant of time, given the emissions caps, an international emissions trading system is organized. In order to be self-enforcing, the emissions caps and the economic growth paths have to satisfy a noncooperative equilibrium condition. We describe this two-level game structure mathematically and give the necessary optimality conditions that must be satisfied by the equilibrium solution under the coupled global emission constraint.

This paper deals with a definition of intergenerational equity in a stochastic game formulation. We propose a piecewise deterministic control model where the control is exerted by a succession of generations, each having a random life duration. Each generation has a concern in both the expected reward received during its own life and the expected reward that will accrue to the next generation when it will take control at the end of the present generation’s life. An intergenerational equilibrium is defined. The model is then specialized to the case of exponential random life duration and stationary state equations. A complete characterization of the equilibrium solution is proposed through the use of a family of auxiliary infinite horizon control problems. A numerical approximation method is proposed. The model and the equilibrium concepts are then used in the context of an integrated assessment model of global climate change impacts.

We investigate a differential game motivated by a problem in mathematical finance. This game displays two interesting features. On the one hand, one of the players, ursuer say, may, and will, use infinitely large controls, i.e., impulses, producing “jumps” in the state variables. Standard optimal trajectories are made of such a jump followed by a “coasting period” where exerts no control. This leads to barriers of a somewhat new type. But because the cost of jumps is only proportional to their amplitude, some singular optimal trajectories arise where uses an intermediary control, nonzero but finite. (In classical impulse control, there is a minimum positive cost to any use of the control, forbidding such a mixed situation.)

On the other hand, the complete solution of the game exhibits a type of singularity, the existence of which had long been conjectured (noticeably by Arik Melikyan in discussions with the first author) but, as far as we know, never shown in actual examples: a two-dimensional focal manifold traversed by noncollinear optimal fields depending on the control used by vader. It is on this manifold that intermediary controls for arise.

Finally, we show that the Isaacs equation of a discrete-time version of the problem provides a discretization scheme that converges to the value function of the differential game. This is done through the investigation of a (degenerate) quasi-variational inequality and its viscosity solution, with the help of an equivalent, but nonimpulsive, differential game—a method of interest per se that we credit to Joshua—to which we apply essentially the classical method of Capuzzo Dolcetta extended to differential games by Pourtallier and Tidball, with some technical adaptations.

This chapter analyzes a differential game model of a two-member marketing channel. A manufacturer invests in national advertising with the purpose of improving (or sustaining) the image of one of her brands, and her retailer makes local promotions for the brand. The game is played à la Stackelberg with the manufacturer as leader. We characterize and compare equilibria for two scenarios. In the first one, the manufacturer designs an incentive strategy to affect the retailer’s promotion strategy with the objective of maximizing the total channel profit. In the second, the manufacturer’s objective is the maximization of her own payoff.

This chapter studies the farsighted behavior of firms in Cournot and Bertrand duopoly markets. The solution concepts used here are the von Neumann-Morgenstern stable set with indirect domination and the consistent set. Principal findings are: (1) in both Cournot and Bertrand duopoly markets, the largest consistent set consists of all possible outcomes, and (2) the stable set with indirect domination yields firms’ joint profit maximization in a Cournot duopoly, and monopoly pricing by two firms in a Bertrand duopoly. In both duopoly markets, the stable set with indirect domination leads to efficient outcomes for the firms.