International Game Theory Review

In this paper, we analyse three Japanese coalition cabinets organised since July 1993, by evaluating parties' power for possible alternative cabinets with Owen's coalition value. In these cabinets, certain parties played a crucial role to determine the cabinet coalition structure. The analysis shows that each of these parties made a good decision for itself in terms of the coalition value, and that the value can be a good prediction of party power.

A weighted average worth per capita formula is presented for any semivalue of a TU game. Further, this formula is used to derive a characterisation of the class of games with the property that a given semivalue belongs to the power core of the game, by means of a linear system of inequalities. It is shown that for the Shapley value, the only efficient semivalue, this system reduces to the system already obtained by Inarra and Usategui. The potential approach is also used even for the more general case of values possessing a potential. A direct proof shows that for a value possessing a potential, the value of a game is in the power core relative to this value, if and only if the potential game is weak average convex. From this result, it follows that for a game and each of its subgames the value possessing a potential is in the corresponding power cores, if and only if the potential game relative to the value is average convex. This is an extension of the result obtained by Marin–Solano and Rafels for the Shapley value, proved by using the dividend form of the game.

The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the relevant cost function is a linear function, then the common pool games are convex games. The convexity, however, fails whenever cost functions are arbitrary. We present sufficient conditions involving the cost functions (like weakly decreasing marginal costs as well as weakly decreasing average costs) and the average joint production function in order to guarantee the convexity of the common pool game. A similar approach is effective to investigate a relaxation of the convexity property known as the average-convexity property for a cooperative game. An example illustrates that oligopoly games are a special case of common pool games whenever the average joint production function represents an inverse demand function.

In models of aspiration-based reinforcement learning, agents adapt by comparing payoffs achieved from actions chosen in the past with an aspiration level. Though such models are well-established in behavioural psychology, only recently have they begun to receive attention in game theory and its applications to economics and politics. This paper provides an informal overview of a range of such theories applied to repeated interaction games. We describe different models of aspiration formation: where (1) aspirations are fixed but required to be consistent with longrun average payoffs; (2) aspirations evolve based on past personal experience or of previous generations of players; and (3) aspirations are based on the experience of peers. Convergence to non-Nash outcomes may result in either of these formulations. Indeed, cooperative behaviour can emerge and survive in the long run, even though it may be a strictly dominated strategy in the stage game, and despite the myopic adaptation of stage game strategies. Differences between reinforcement learning and evolutionary game theory are also discussed.

In this paper, we unify various axiomatisations of the core of TU games by means of consistency with respect to different definitions of reduced games. First, we introduce a general definition of reduced games including the reduced games due to Davis and Maschler (1965), Moulin (1985), and Funaki (1995) as special cases. Then, we provide a general theorem from which the characterisations due to Peleg (1986), Tadenuma (1992), and Funaki (1995) can be obtained. Our general theorem clarifies how the three characterisations of the core differ and are related.

In this paper, I discuss the formulation and some applications of a framework called "hierarchy games". Hierarchy games are a game theoretical framework in which two or more games interact with one another. The interaction among games can be best described by the following two characteristics: (1) the outcome of a lower-level game could restrict the available actions of a player in higher-level. (2) the payoff of a higher-level player is shared by lower-level players. The above ideas were first proposed by Hausken in 1995. The paper attempts to develop further those ideas. First, some parts of the framework are defined more rigorously than Hausken's formulation. Secondly, some applications of the framework to the field of International Relations are discussed.

Let Y(t), t∈[0,1], be a stochastic process modelled as dY_t=θ(t)dt+dW(t), where W(t) denotes a standard Wiener process, and θ(t) is an unknown function assumed to belong to a given set Θ⊂L²[0,1]. We consider the problem of estimating the value ℒ(θ), where ℒ is a continuous linear function defined on Θ, using linear estimators of the form <m,y>=∫m(t)dY(t), m∈L²[0,1]. The distance between the quantity ℒ(θ) and the estimated value is measured by a loss function. In this paper, we consider the loss function to be an arbitrary even power function. We provide a characterisation of the best linear mini-max estimator for a general power function which implies the characterisation for two special cases which have previously been considered in the literature, viz. the case of a quadratic loss function and the case of a quartic loss function.

One of the first and perhaps the most well-known polynomially solvable special case of the traveling salesman problem (TSP) is the Gilmore-Gomory case (G-G TSP). Gilmore and Gomory presented an interesting patching algorithm for this case with a fairly non-trivial proof of its validity. Their work has motivated a great deal of research in the area leading to various generalisations of their results and thereby identification of fairly large polynomially solvable subclasses of the TSP. These results form a major portion of the literature on solvable cases of the TSP. In this paper, we survey the main results on solvable cases of the TSP which are direct generalisations of the G-G TSP and/or the Gilmore-Gomory patching scheme.

In this paper, we survey the recent literature on computing the value vector and the associated optimal strategies of the players for special cases of zero-sum stochastic games, or in computing a Nash equilibrium point and the corresponding stationary strategies of the players for special cases of nonzero-sum stochastic games, using finite-step algorithms based on pivoting. Examples of finite-step pivoting algorithms are the various simplex-type algorithms, such as the primal simplex or dual simplex method for solving the linear programming problem or Lemke's or Lemke-Howson's algorithm for solving the linear complementarity problem. Also included are Lemke-type algorithms for solving various generalisations of the linear complementarity problem. The survey also includes a few new results and observations.