International Game Theory Review

A system of two components is analyzed as a two-period game. After period 1 the system can be fully operational, in two states of intermediate degradation, or fail. Analogously to changing failure rates in dependent systems analyzed with Markov analysis, unit costs of defense and attack, and contest intensities, change in period 2. As the values of the two intermediate states increase from zero which gives the series system, towards their maxima which gives the parallel system, the defender becomes more advantaged, and the attacker more disadvantaged. Simulations illustrate the players' efforts in the two time periods and utilities dependent on parametric changes. The defender withdraws from defending the system when the values of both degraded states are very low. The attacker withdraws from attacking the system when the values of both degraded states are very high. In the benchmark case the defender prefers the one-period game and the attacker prefers the two-period game, but if the attacker's unit cost of attack is large for one component, and the value of the degraded system with this component operational is above a low value, the defender prefers the two-period game to obtain high utility in period 2 against a weak attacker. When the values of the degraded states are above certain low values, the players exert higher efforts in period 1 of a two-period game than in a one-period game, as investments into the future to ensure high versus low reliability in period 2.

In moving from finite-action to infinite-action games, standard refinements of the Nash equilibrium concept cease to satisfy certain "natural" properties. For instance, perfect equilibria in compact, continuous games need not be admissible. This paper highlights additional properties of two standard refinement specifications that are not inherited by supersets of the set of finite games. The analysis reveals the following about the behavior of perfectness and strategic stability within a class of (possibly) discontinuous games: (1) Equilibria that assign positive probability to the interior of the set of strategies weakly dominated for some player can be chosen; (2) nonadmissible equilibria need not be ruled out when they are weakly dominated by admissible perfect equilibria; and (3) nonadmissible equilibria may be selected when admissible equilibria are ruled out.

This paper studies situations in which companies can cooperate in order to decrease the earliest completion time of a project that consists of several tasks. This is beneficial for the client who wants the project to be completed as early as possible. The client is willing to pay more for an earlier completion time. The total payoff must be allocated among the companies that cooperate. Cooperative game theory is used to model this situation. Conditions for the core of the game to be nonempty are derived. We study a class of project management games for which necessary and sufficient conditions for the nonemptiness of the core can be derived. We will show that a subset of the set of balanced project management games can be partitioned into a class of 1-convex games and a class of big boss games. Expressions for the extreme points of the core, the τ-value, the nucleolus, and the Shapley-value of games in these two classes are derived.

From a special class of TU games with information cost, given by the problem of sharing the costs of facilities among users, we build a noncooperative game in which every player asks for the assessment of whom the users are. We analyze two models, "naming" game and majority decision game: the existence of equilibria is assured since the games are binary and symmetric, and then potential games. Since the games are ex-ante fair, we search a proposal to compensate for ex-post injustice.

In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional space in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibria correspondence and essential games.

We analyze strategic delegation in a Stackelberg model with an arbitrary number, n, of firms. We show that n-1 firms delegate their production decisions and only one firm (the one whose manager is the first mover) does not. The later a manager commits to a quantity, the higher his incentive rate. Letting denote the equilibrium payoff of the firm whose manager commits in the ith stage, we show that . We also compare the delegation outcome of our game with that of a corresponding Cournot oligopoly and show that managers who commit late (early) are given higher (lower) incentive rates than managers in the Cournot market.

Despite the popularity of auction theoretical thinking, it appears that no one has presented an elementary equilibrium analysis of the complete information first-price sealed-bid auction mechanism when the bidding space has a finite grid. This paper aims to remedy that omission. We show that there always exists a "high price equilibrium" which can be considered "the intuitive solution" (an agent with the highest valuation wins the auction bidding at the second highest valuation). Although there might be other "low price equilibria," we also show that when there are two bidders "the intuitive solution" is the unique limiting equilibrium when the grid size goes to zero and ties are randomly broken.