International Game Theory Review

Coopetition is defined as the existence of simultaneous competition and cooperation between the same set of players, leading to entanglement of payoffs and actions of the players. This paper provides insights into the game theoretical application of quantum games to model simultaneity and entanglement that occur in coopetition. Modeling as a quantum game also allows for a larger action space and hence new equilibrium that may not have existed earlier. The impact of the level of entanglement on the equilibrium of the game can also be studied. We demonstrate the same through an example of two players who currently compete in the domestic market and are considering cooperating simultaneously in the international market. They need to determine the equilibrium strategy to adopt under coopetition that maximizes their payoffs. We also arrive at how to ensure that the quantum strategy is the equilibrium strategy for both players, namely, how to design the quantum strategy and how to define the unitary operator.

Games with endogenous transition probabilities and endogenous stage payoffs (or ETP–ESP games for short) are stochastic games in which both the transition probabilities and the payoffs at any stage are continuous functions of the relative frequencies of all past action combinations chosen.

We present methods to compute large sets of jointly-convergent pure-strategy rewards in two-player ETP–ESP games with communicating states under the limiting average reward criterion. Such sets are useful in determining feasible rewards in a game, and instrumental in obtaining the set of (Nash) equilibrium rewards.

In this paper, we investigate a dilemma of employing silent mode and communication mode by an unmanned aerial vehicle (UAV) in communication with its controller. In many applications, a UAV communicates with a controller to receive instructions or accurate positioning, but such active communication poses a threat that the UAV can be hijacked through spoofing. On the other hand, during a silent mode (when the UAV does not communicate with the controller), the UAV is safe from spoofing, but is not receiving updates or other important data, and can degrade the overall UAV mission. To gain insight into the UAV risk versus benefit tradeoff, a simple game-theoretic model is presented. Additionally, this paper investigates how incomplete information about the capability of the controller to quickly learn the adversary’s attack and adjust its strategy accordingly can impact the equilibrium strategies. In contrast to regular-type capability, when both the rivals maximize their payoffs simultaneously, the capability of the controller to quickly learn is modeled by having the controller apply the best-response strategy. We model this problem using a Bayesian game, where the adversary knows only a priori probabilities about what capability the controller has. Dependence of the equilibrium strategies on these a priori probabilities is illustrated.

We study the effects of endogenous cost formation in the classic Cournot oligopoly through an extended two-stage game. The competing Cournot firms produce low-cost but limited quantities of a single homogeneous product. For additional procurements, they may refer to a revenue-maximizing supplier who sets a wholesale price prior to their orders. We express this chain as a two-stage game and study its equilibrium under two different information levels: complete and incomplete information on the side of the supplier about the actual market demand. In the deterministic case, we derive the unique subgame-perfect Nash equilibrium for different values of the retailers’ capacity levels, supplier’s cost and market demand. To study the incomplete information case, we model demand uncertainty via a continuous probability distribution. Under mild assumptions, we characterize the supplier’s optimal pricing policy as a fixed point of a proper translation of his expectation about the orders that he will receive from the retailers. If this expectation is decreasing in his price, then such an optimal policy always exists and is unique. Based on this characterization, we are able to proceed with comparative statics and sensitivity analysis, both analytically and numerically. Incomplete information gives rise to market inefficiencies because the supplier may ask for a too high price. Increasing supplier’s cost results in increasing wholesale prices, decreasing orders from the retailers and hence decreasing consumer surplus. Increasing retailers’ production capacities results in decreasing wholesale prices and increasing consumer surplus. Finally, as the number of second-stage retailers increases, the supplier’s profit may initially rise but eventually drops.

This paper considers the Gale–Shapley model with interdependent preferences. Women’s preferences over men are common knowledge but whether or not a man is acceptable depends on the preferences of men which are private information. It is shown that no ex-post incentive-compatible and ex-post stable matching rules exist. A characterization of ex-post incentive-compatible, ex-post individually rational and ex-post nonbossy matching rules in terms of modified priority rules is provided.

One of the key features which promote growth of industrial clusters is collaboration among firms within such clusters. Collaboration among firms leads to the formation of networks. Stability of these networks is vital to the sustainability of the particular firms. In this paper, we model a supply chain network where a set of downstream firms (players) source inputs from upstream firms (players) who manufacture goods, add value to the products and resell them. The upstream firms produce identical goods and compete on quantities to sell these goods to the downstream firms. The upstream firms procure goods from the downstream firms and sell them. Additionally, upstream firms network among themselves so as to reduce their costs. We model this setting as a two-stage $n$-player strategic network formation game. Firms decide their links before competing on quantities in the second stage of the game. Using the defined model, we derive equilibrium quantities and profits as a function of the network structure and number of firms. Following which we analyze the conditions under which different stable network emerge. Our analysis brings forth several interesting insights such as higher connections among downstream players lead to increased profits for upstream manufacturers. From the network stability perspective, we obtain the conditions under which regular, star, etc. network structures are pairwise and bilaterally stable. Furthermore, we also find the conditions under which core–periphery network structures emerge and are stable.

We examine a dynamic two-stage incumbent-challenger model of internal conflict, where the government, i.e., the incumbent, is in power, while the rebel challenges the government in a bid to capture state power. The central issue is the trade-off between development and security-based measures in countering such rebellion activity. We find that while an exogenous increase in development decreases the level of rebellion activity, it increases the level of security-based measures by the government whenever the rebel is ‘dominant’ to begin with. Further, if the rebel is dominant, then, with the rebel becoming stronger (i.e., becoming more cost efficient), the level of rebel activity increases, while the security-based measures by the government is lowered. Thus, our analysis suggests that the trade-off is a nuanced one. This framework also allows us to reconcile some divergent results in the empirical literature regarding the effect of development works on conflict.

Zero-sum two-person discounted semi-Markov games with finite state and action spaces are studied where a collection of states having Perfect Information (PI) property is mixed with another collection of states having Additive Reward–Additive Transition and Action Independent Transition Time (AR-AT-AITT) property. For such a PI/AR-AT-AITT mixture class of games, we prove the existence of an optimal pure stationary strategy for each player. We develop a policy improvement algorithm for solving discounted semi-Markov decision processes (one player version of semi-Markov games) and using it we obtain a policy-improvement type algorithm for computing an optimal strategy pair of a PI/AR-AT-AITT mixture semi-Markov game. Finally, we extend our results when the states having PI property are replaced by a subclass of Switching Control (SC) states.

This research develops a decision support for strategic pricing and aggregate production distribution planning for a small-scale supplier intending to penetrate into a potential market engendered by a single buyer. A novel mixed integer bilevel programming model is proposed to formulate the problem in which the supplier is considered as a leader and the buyer is a follower. The proposed model subsumes the assessment of demand share against the price quotation, enabling the supplier to prepare an aggregate production distribution plan accordingly. An integer coded genetic algorithm is used to solve the model and its implementation is exhibited through a test scenario.

In this contribution, a consensus model is proposed to acquire a unified and converging solution of multi-criteria large group decision making problems. Unlike the iterative process and feedback mechanism based models, the suggested approach features the optimization theory to establish the consensus in one go only among the efficient experts. The time salvation characteristic of the model makes it expedient for the emergency planning and management decision problems. The algorithm is validated using the hurricane evacuation notification time problem of United States.

This paper presents an EPQ model which illustrates imperfect production and imperfect inspection processes for items that are subject to a constant rate of deterioration. The model considers two types of inspection errors, namely, Type I error of falsely screening out a proportion of nondefects, thereby passing them on for rework and Type II error of falsely not screening out a proportion of defects, thus selling those to customers which results in defect sales returns. The screened and returned items are then reworked and the proportion that could not be reworked successfully is scrapped. Shortages are allowed and are completely backlogged. Finally, we calculate the optimal production lot size and the optimal backordering quantity in order to minimize the total inventory cost per unit time. A numerical example is also considered to exemplify the obtained theoretical results which is followed by the complete sensitivity analysis of the involved parameters for even better managerial insights.