International Game Theory Review

The concert queueing problem corresponds to determining the equilibrium arrival profile of non-cooperative customers selecting their arrival times to a queue where the service opens at a specified time. The customers are allowed to arrive before or after this time. This problem has a variety of queuing applications including how people queue at airport, movie theaters, passport offices, ration lines, etc. This also captures the settings where large computational jobs are sent to servers that open for service at a specified time. Substantial literature is devoted to studying the more tractable fluid version of this problem, that is, each customer is considered an infinitesimal particle, resulting in a non-atomic game between customers. This allows for explicit determination of the unique equilibrium arrival profile in many such settings as well as the associated socially optimal centralized solution. The knowledge of both then allows the computation of price of anarchy (PoA) in the system. The literature thus far focuses on queues with the first come first serve (FCFS) service discipline. In this paper, we again consider the fluid regime and extend the analysis to the case where the service discipline is random order service (ROS). This is equivalent to the practically equally important processor sharing regime when the service times are exponential. The latter is relevant in computational settings while the former is a good approximation to settings where a customer is selected more or less at random by the server.

Horizontal supply chains is the term used when suppliers competing at a particular level of the chain form a coalition to benefit from their cooperation rather than the usual competitive strategies used by them to become part of the supply chain. Such horizontal cooperation among competitors is studied by Wood, using qualitative research methodology, based on case studies done in New Zealand. The term "coopetition" is used in the literature to describe such a cooperative behavior among competitors. In this paper we examine the coopetition phenomenon from a game theoretic perspective and give a model that brings out the equilibria that will lead to optimal participation among the coalition partners. The model considers a set of growers who can choose to form a coopetitive alliance to market their production in some external regions, while competing within the internal regions. By means of a general analytical framework of competition, we show the strategies that could provide solutions, in a coopetitive perspective, for the growers. These solutions offer a win–win outcome for the growers, letting them share the pie fairly within a growth path of games. We determine the proportion of resources they'll use and how the gain will be shared.

We model and analyze strategic interaction over time in a duopoly. Each period the firms independently and simultaneously take two sequential decisions. First, they decide whether or not to advertise, then they set prices for goods which are imperfect substitutes. Not only the own, but also the other firm's past advertisement efforts affect the current "sales potential" of each firm. How much of this potential materializes as immediate sales, depends on current advertisement decisions. If both firms advertise, "sales potential" turns into demand, otherwise part of it "evaporates" and does not materialize. We determine feasible rewards and equilibria for the limiting average reward criterion. Uniqueness of equilibrium is by no means guaranteed, but Pareto efficiency may serve very well as a refinement criterion for wide ranges of the advertisement costs.

Mathematical foundations of conflict resolutions are deeply rooted in the theory of cooperative and non-cooperative games. While many elementary models of conflicts are formalized, one often raises the question whether game theory and its mathematically developed tools are applicable to actual legal disputes in practice. We choose an example from union management conflict on hourly wage dispute and how zero sum two person game theory can be used by a judge to bring about the need for realistic compromises between the two parties. We choose another example from the 2000-year old Babylonian Talmud to describe how a certain debt problem was resolved. While they may be unaware of cooperative game theory, their solution methods are fully consistent with the solution concept called the nucleolus of a TU game.

In this paper, we examine several options for modeling local interactions within the framework of evolutionary game theory. Several examples show that there is a major difference between population dynamics using local dynamics versus global dynamics. Moreover, different modeling choices may lead to very diverse results.

In this paper, we have developed a new method to solve bi-level quadratic linear fractional programming (BLQLFP) problems in which the upper-level objective function is quadratic and the lower-level objective function is linear fractional. In this method a BLQLFP problem is transformed into an equivalent single-level quadratic programming (QP) problem with linear constraints by forcing the duality gap of the lower-level problem to zero. Then by obtaining all vertices of the constraint region of the dual of the lower-level problem, which is a convex polyhedron, the single-level QP problem is converted into a series of finite number of QP problems with linear constraints which can be solved by any standard method for solving a QP. The best among the optimal solutions gives the desired optimal solution for the original bi-level programming (BLP) problem. Theoretical results have been illustrated with the help of a numerical example.

We consider a two player finite state-action general sum single controller constrained stochastic game with both discounted and average cost criteria. We consider the situation where player 1 has subscription-based constraints and player 2, who controls the transition probabilities, has realization-based constraints which can also depend on the strategies of player 1. It is known that a stationary Nash equilibrium for discounted case exists under strong Slater condition, while, for the average case, stationary Nash equilibrium exists if additionally the Markov chain is unichain. For each case we show that the set of stationary Nash equilibria of this game has one to one correspondence with the set of global minimizers of a certain nonconvex mathematical program. If the constraints of player 2 do not depend on the strategies of player 1, then the mathematical program reduces to a quadratic program. The known linear programs for zero sum games of this class can be obtained as a special case of above quadratic programs.

This study seeks to analyze the impact of governmental regulations on the pollution level in a duopoly framework with endogenous market structure. We consider a dirty industry which involves two asymmetric firms, an MNC and a domestic firm, producing a homogenous product, where the MNC is so efficient that in the absence of a joint venture the MNC firm will act as a monopolist. We use a game theoretic framework to demonstrate that an increase in abatement cost, arising out of stricter government regulations, could trigger a regime-switch from monopoly to joint venture (or from joint venture to monopoly), and consequently may increase pollution. Turning to the welfare analysis, we find that the constrained first best outcome always involves joint venture formation. Given a market structure, we find that the optimal emission tax is always less than the marginal social damage. We then demonstrate that if the synergistic effect (SE) is large and the industry is neither very dirty, nor very clean, then the constrained first best outcome can be implemented by setting the abatement tax appropriately. Otherwise the constrained first best outcome cannot be implemented.

This paper develops alternative models explaining why households with credit need to finance their projects (enterprises) avoid formal credit. More importantly it argues that the problem of avoidance of formal credit and ensuring credit access is not necessarily restricted to the small borrower or borrowers with inefficient projects. Delay cost and personal loan transaction cost may also cause highly productive projects or larger projects shying away from formal credit in spite of low interest rates. Some of the policy implications of the above findings are also discussed.

Promotion plays an important role in determining fate of a product. It voices product qualities and persuades potential customers to make purchases. In todays diversified markets every customer has individual needs and preferences. This calls for market segmentation which facilitates companies to adopt customer driven marketing. Product is also promoted using mass promotion to influence larger markets and segments with a spectrum effect. Existing literature in promotion resource allocation optimization evades distinction in two types of promotion strategies while allocating resources and primarily focuses on either of them statically. In this paper, we formulate an optimization model which dynamically allocates differentiated and mass promotional resources in segments to maximize sales under budgetary and minimum market share aspiration constraint on each segment as well as on total market share including repeat purchase behavior. Planning horizon is divided into multi-periods, adoption pattern is studied in each period and then resources are allocated attuned to current market behavior. Dynamic allocation provides a way to track the market potential expansion due to promotion and plan the allocation for the uncaptured potential. The proposed optimization model is NP hard and very challenging to solve. Solution methodology is presented with practical application based on real-time data using differential evolution algorithm.

Two-person finite semi-Markov games (SMGs) are studied when the transition probabilities and the transition times are controlled by one player at all states. For the discounted games in this class, we prove that the ordered field property holds and there exist optimal/Nash equilibrium stationary strategies for the players. We illustrate that the zero-sum SMGs where only transition probabilities are controlled by one player, do not necessarily satisfy the ordered field property. An algorithm along with a numerical example for the discounted one player control zero-sum SMGs is given via linear programming. For the undiscounted version of such games, we exhibit with an example that if the game ceases to be unichain, an optimal stationary or Markov strategy need not exist, (though in this example of a one-player game we exhibit a semi-stationary optimal strategy/policy). Lastly, we prove that if such games are unichain, then they possess the ordered field property for the undiscounted case as well.