International Game Theory Review

We deal with zero-sum stochastic games. We demonstrate the importance of stationary strategies by showing that stationary strategies are better (in terms of the rewards they guarantee for a player, against any strategy of his opponent) than (1) pure strategies (even history-dependent ones), (2) strategies which may use only a finite number of different mixed actions in any state, and (3) strategies with finite recall. Examples are given to clarify the issues.

A quitting game is a sequential game where each player has two actions: to continue or to quit, and the game continues as long as no player quits.

For every continuation payoff x we assign a one-shot game, where the payoff if everyone continues is x. We study the dynamics of the correspondence that assigns to every continuation payoff the set of equilibrium payoffs in the corresponding one shot game.

The study presented here has an implication on the approach one should take in trying to prove, or disprove, the existence of an equilibrium payoff in n-player stochastic games. It also shows that the minimal length of the period of a periodic δ-equilibrium in three-player quitting games needs not be uniformly bounded for δ>0.

In many markets, competing but differentiated firms offer a product line in order to target each product to a different type of customer. Under competition, firms, while trying to target different products to different segments, are also interested in "stealing" customers from the competitors and, in particular, customers from the most profitable segments. How should a profit-maximising firm allocate the advertising budget along a competitive product line? Devel oping a closed-loop time-variant Nash equilibrium strategy for a multi-player multi-product advertising game, we find the determinants of the optimal advertising budget allocation in a product line in an oligopoly growing market. Moreover, for a symmetric competition in a fixed market, we derive an analytic feedback time-variant Nash equilibrium strategy. Marketing implications regarding the firm's strategic orientation in product preference advertising spending, as well as comparison to rivals' spending, are discussed. Finally, we show that using a single-product advertising game instead of a multi-product advertising game, leads to over-advertising.

Two new axioms, additivity of additional bonus (AAB) and reduced game monotonicity (RGM), are introduced. AAB states that the players can gain an additional bonus after they achieved an agreement; on the other hand, if the bargaining fails then they get nothing. With its help, we characterise the lexicographic egalitarian solution by individual rationality (IR), AAB and consistency (CON). The other axiom, RGM, is a weaker axiom than CON and strong monotonicity (SMON), respectively. Using Pareto optimal (PO), IR, AAB and RGM, the second characterisation of the lexicographic egalitarian solution is presented.

We consider a firm that wishes to maximise the profits coming from the sale of a new product or technology by determining an optimal price and advertising strategy. A public authority wishes to accelerate and stimulate the adoption of the new product by using a budget to give price subsidies directly to the consumers. The problem is set up as a Stackelberg differential game.

The approach introduced by Gromb, Ponssard and Sevy (GPS) for dynamic entry games provides satisfactory results in the case of price competition but leaves the issue pending for quantity competition. This paper proposes a market attribution rule that restores the desired properties: average cost pricing in the symmetric case and the selection of the most efficient firm when asymmetry is introduced.

In this paper, a new value for set games, named co-marginalistic contribution value, is characterised by the standard axioms of global efficiency and equal treatment property, and another axiom of co-coalitional marginalistic monotonicity, which is a modification of the axiom of monotonicity. The co-marginalistic contribution value for set games is analogous to the solidarity value for n-person TU-games. Since the co-marginalistic contribution value does not satisfy the axiom of additivity, the proof of the characterisation is much different from that for TU-games.