International Game Theory Review

The article analyzes how a defender determines a balance between protecting an object (passive defense) and striking preventively against an attacker seeking to destroy the object (active defense). The attacker analogously determines a balance between attacking and protecting against the preventive strike. The defender makes its decision about striking preventively based on its estimate of the probability of being attacked. In both cases of preventive strike and no preventive strike, the defender anticipates the most harmful attacker's strategy. The influence of the ratio between the player's resources and the contest intensities on the solution of the game is analyzed.

This article studies how a mechanism designer can influence games by promising payments to the players depending on their mutual choice of strategies. First, we investigate the cost of implementing a desirable behavior and present algorithms to compute this cost. Whereas a mechanism designer can decide efficiently whether strategy profiles can be implemented at no cost at all our complexity analysis indicates that computing an optimal implementation is generally NP-hard. Second, we introduce and analyze the concept of leverage in a game. The leverage captures the benefits that a benevolent or a malicious mechanism designer can achieve by implementing a certain strategy profile region within economic reason, i.e., by taking the implementation cost into account. Mechanism designers can often manipulate games and change the social welfare by a larger extent than the amount of money invested. Unfortunately, computing the leverage turns out to be intractable as well in the general case.

In a strategic coalitional game, we consider the relations among four cores α, β, γ, and the one we call δ which is obtained by slightly weakening the conjectural cooperative equilibria due to Currarini and Marini. We show that the α-core and the γ-core are refined by the δ-core; and, moreover that if every player has a dominant strategy, the β-core is refined by the γ-core, so that the four cores refine themselves in the greek alphabetical order. Two economic games will be considered to show that the refinement of the α-core can vary from the weakest to the strongest. While the four cores are equal in the pure exchange game, a radical reduction of the α-core is obtained in the commons game, a simple version of the Cournot game, bringing about a single strategy profile as the δ-core.

We study a non-cooperative model of unilateral network formation. Derks et al. [2008b] prove the existence of local-Nash and global-Nash networks for games with payoff functions that satisfy a framework of axiomatic properties. These properties are inspired by the one-way flow model, which is characterized by the following payoff structure. Each agent pays a cost for each formed link and receives profits from being connect to other agents. In this paper we fully characterize the payoff functions in the one-way flow model that satisfy all properties. We show that under certain conditions, payoff functions with heterogeneous link costs and heterogeneous profits satisfy all properties for which the existence of local-Nash networks is proved. Furthermore, we show that all payoff functions with owner-homogeneous link costs and heterogeneous profits satisfy all properties, and therefore imply the existence of global-Nash networks.

In simultaneous ascending price auctions with heterogeneous goods Brusco and Lopomo [2002] derive collusive equilibria, where bidders divide objects among themselves, while keeping the prices low. Considering a simultaneous ascending price auction with a fixed deadline, i.e. the hard close auction format, a prisoner's dilemma situation results and collusive equilibria do not longer exist, even for only two bidders. Hence, we introduce a further reason for sniping behavior in Hard Close auctions, i.e. to appear to collude early in the auction and to defect at the very last moment.

In many instances of price discrimination, a seller of an item is in possession of signals from competing buyers regarding their private valuation for the item. If the seller uses this information to price discriminate against the buyer, buyers would correspondingly modify their signalling strategy. Our paper shows that the seller can gain by sometimes strategically ignoring the information contained in the signals and pricing the item in a non-discriminatory way. This "mixed" strategy induces buyers to send more informative signals in equilibrium than if the seller were to always price discriminate. Thus the seller can offset any revenue loss in states where he ignores information by the gains made in states where he can price discriminate more effectively due to the larger amount of information now communicated in the signals.

Stackelberg-like games show a situation where there is a clear advantage in moving first. In a thought provoking article, Bagwell [1995] shows that this advantage may not be robust against imperfect observations of the first move. We explore these ideas in the context of forward induction in three classic games, namely, the outside option game, the game of burning a dollar before the battle of the sexes and the beer-quiche game.

This paper investigates core stability of cooperative (TU) games via a fuzzy extension of the totally balanced cover of a cooperative game. The stability of the core of the fuzzy extension of a game, the concave extension, is shown to reflect the core stability of the original game and vice versa. Stability of the core is then shown to be equivalent to the existence of an equilibrium of a certain correspondence.