International Game Theory Review

The objective of the paper is to study how wholesale price and revenue sharing contracts affect operations and marketing decisions in a supply chain under different dynamic informational structures. We suggest a differential game model of a supply chain consisting of a manufacturer and a single retailer that agree on the contract parameters at the outset of the game. The model includes key operational and marketing activities related to a single product in the supply chain. The manufacturer sets a production rate and the rate of advertising efforts while the retailer chooses a purchase rate and the consumer price. The state of the game is summarized in the firms’ backlogs and the manufacturer’s advertising goodwill. Depending on whether the supply chain members have and share state information, they may either make decisions contingent on the current state of the game (feedback Nash strategy), or precommit to a plan of action during the whole game (open-loop Nash strategy). Given a contract type, the impact of the availability of information regarding the state of the game on the firms’ decisions and payoffs is investigated. It is shown that double marginalization can be better mitigated if the supply chain members adopt a contingent strategy under a wholesale price contract and a commitment strategy under a revenue sharing contract.

We consider situations, in which socially important goods (like transportation capacity or hospital beds) are supplied by independent economic agents. There is also a regulator that believes that constraining the goods delivery is desirable. The regulator can compute a constrained Pareto-efficient solution to establish optimal output levels for each agent. We suggest that a coupled-constraint equilibrium (also called a “generalized” Nash or “normalized” equilibrium à la Rosen) may be more relevant for market economies than a Pareto-efficient solution. We examine under which conditions the latter can equal the former. We illustrate our findings using a coordination problem, in which the agents’ outputs depend on externalities. It becomes evident that the correspondence between an efficient and equilibrium solutions cannot be complete if the agents’ activities generate both negative and positive externalities at the same time.

The question of energy management is a major engineering challenge in any wireless communication system that is constrained by finite battery resources. In this paper, we address the problem of transmit power control in a multi-user wireless network with a single base station and random time-varying channels transmitting in parallel and interfering between each other. We suggest a stochastic particle system for studying the game of control; specifically, the channels are modeled as purely discontinuous Markov processes with known characteristics. The signal to interference plus noise ratio (SINR) determines the interactions among particles. Dimensionality reduction of the multi-objective optimization problem relies on chaos propagation, i.e., on the fact that the independence of particles persists in time as and when their number becomes large. And then we solve the optimal control problem for one representative of the particle system. Furthermore, we develop a martingale approach for an alternative open-loop optimal control instead of the feedback one since the latter is not computationally feasible.

A generalization of the class of bargaining problems examined by Engwerda and Douven [(2008) On the sensitivity matrix of the Nash bargaining solution, Int. J. Game Theory 37, 265–279] is studied. The generalized class consists of nonconvex bargaining problems in which the feasible set satisfies the requirement that the set of weak Pareto-optimal solutions can be described by a smooth function. The intrinsic comparative statics of the aforesaid class are derived and shown to be characterized by a symmetric and positive semidefinite matrix, and an upper bound to the rank of the matrix is established. A corollary to this basic result is that a Nash bargaining solution is intrinsically a locally nondecreasing function of its own disagreement point. Other heretofore unknown results are similarly deduced from the basic result.

We consider service providers (e.g., contractors) who bid for undertaking a large project — reverse auctions. As there is a risk that the lowest bidder will not be able to complete the project on budget or time, the customer, often a government agency, wishes to incorporate prior information on the bidders reliabilities into the choice of winning bid. We consider the use of official ratings of bidders, which are common knowledge. The customer is assumed to select the bidder for which the ratio of bid to rating is the lowest. A bidder assumes that each other bidder’s bid is the sum of its private value, the ratio of this value to its rating and the inverse of the rating. We characterize the equilibrium bids of two bidders, of $n$ symmetric bidders and of three nonsymmetric bidders, and provide comparative statics and examples. We also discuss a scenario where all ratings are known only to the customer, and each bidder knows only its own rating.

A cooperative game with transferable utility (TU game) captures a situation in which players can achieve certain payoffs by cooperating. We assume that the players are part of a hierarchy. In the literature, this invokes the assumption that subordinates cannot cooperate without the permission of their superiors. Instead, we assume that superiors can force their subordinates to cooperate. We show how both notions correspond to each other by means of dual TU games. This way, we capture the idea that a superiors’ ability to enforce cooperation can be seen as the ability to neutralize her subordinate’s threat to abstain from cooperation. Moreover, we introduce the coercion value for games with a hierarchy and provide characterizations thereof that reveal the similarity to the permission value.