International Game Theory Review

We show that the Aumann–Davis–Maschler bargaining set and the Mas-Colell bargaining set of a non-leveled NTU game that is either ordinal convex or coalition merge convex coincides with the core of the game. Moreover, we show by means of an example that the foregoing statement may not be valid if the NTU game is marginal convex.

In this paper, we study TU-games with coalition structure and propose an approach for determining a stable coalition structure solving a stochastic game of a special form. Using a Nash equilibrium in this game, we draw an analogy between the stable coalition structure and an absorbing state in a Markov chain. In addition, we consider a case of restricted coalitions assuming that not all coalitions are feasible and extend the definition of the stable coalition structure to this case.

We characterize the space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal combinatorial auctions where efficiency is not required. We examine a model with two players and k nonidentical items (2^k outcomes), multidimensional types, private values, non-negative prices, and quasilinear preferences for the players with one relaxation — the players are subject to publicly-known budget constraints. We show that if it is publicly known that the players value the bundles more than the smaller of their budgets then the studied space includes one type of mechanism: autocratic mechanisms (a form of dictatorship). Furthermore, we prove that there are families of autocratic mechanisms that uniquely fulfill the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal. Interestingly the above basic properties are a weaker requirement than it may initially appear, as the property of Pareto optimality in our model of budget-constrained players and non-negative prices do not coincide with welfare maximization, i.e., efficiency as such is a much weaker requirement.

In potential games, the best-reply dynamics results in the existence of a cost function such that each player's best-reply set equals the set of minimizers of the potential given by the opponents' strategies. The study of sequential best-reply dynamics dates back to Cournot and, an equilibrium point which is stable under the game's best-reply dynamics is commonly said to be Cournot stable. However, it is exactly the best-reply behavior that we obtain using the Lyapunov notion of stability in game theory. In addition, Lyapunov theory presents several advantages. In this paper, we show that the stability conditions and the equilibrium point properties of Cournot and Lyapunov meet in potential games.

This paper focuses on situations in several companies each of which has a set of jobs that it has to complete. Each job has a specific starting and ending time and a specific starting and ending point. In order to complete its jobs a company needs to acquire components. There are several types of components. Each job requires exactly one component but not all components are suitable for all jobs. By cooperating, the companies can reduce the costs of acquisition. A component can be used by several companies as long as there is no overlap in the time-intervals of usage by different companies and there is enough time to move the component from where a company has stopped using it to where the next company needs it. A cooperative component acquisition game is constructed to model the cooperation between the companies. This game need not be balanced. Additional properties are introduced that guarantee the game to be totally balanced. We construct an element of the core by using the integer programming formulation of the characteristic function. These games have some relationship with coloring games but we show that results that are valid for coloring games do not hold for them.

A linear nonstationary pursuit problem in which a group of pursuers and a group of evaders are involved is considered under the condition that the group of pursuers includes participants whose admissible controls set coincides with that of the evaders and participants whose admissible controls sets belong to interior of admissible controls set of the evaders. The aim of the group of pursuers is to capture all the evaders. The aim of the group of evaders is to prevent the capture, that is, to allow at least one of the evaders to avoid the rendezvous. It is shown that, if in the game in which all the participants have equal capabilities at least one of the evaders avoids the rendezvous on an infinite time interval, then as a result of the addition of any number of pursuers with less capabilities, at least one of the evaders will avoid the rendezvous on any finite time interval.

A well-known and simple game to model markets is the glove game where worth is produced by building matching pairs. For glove games, different concepts, like the Shapley value, the component restricted Shapley value or the Owen value, yield different distributions of worth. While the Shapley value does not distinguish between productive and unproductive agents in the market and the component restricted Shapley value does not consider imbalancedness of the market, the Owen value accounts for both. As computational effort for Shapley-based allocation rules is generally high, this note provides a computationally efficient formula for the Owen value (and the component restricted Shapley value) for glove games in case of minimal winning coalitions. A comparison of the efficient formulas highlights the above-mentioned differences.