Sharing costs in highways: A game theoretic approach

This paper introduces a new class of games, highway games, which arise from situations where there is a common resource that agents will jointly use. That resource is an ordered set of several indivisible sections, where each section has an associated fixed cost and each agent requires some consecutive sections. We present an easy formula to calculate the Shapley value, and we present an efficient procedure to calculate the nucleolus for this class of games.     

A game theoretic approach to measuring efficiency

Correspondence with a new mathematical programming definition for efficiency as proposed by Charnes, Cooper and Rhodes (CCR) is established by means of game theoretical models. Contact with all of the CCR results is also maintained so that their results extend to our new game theoretic interpretations. The latter proceeds by means of a family of games related to a linear programming problem. The games-to-programming relations which we establish also open new possibilities for further relations between families of games and linear programs.     

Knowledge sharing in communities of practice: A game theoretic analysis

This research applies game theory to analyze the incentives of knowledge-sharing activities in various types of communities of practice (COPs), characterized by individual profiles and decision structures. Indeed, individual decision making results in the under-provision of knowledge; however, the benefit of knowledge sharing may be raised by IT investment and suitable incentive mechanisms we study here. In general conditions, improving communication and collaboration technologies should be prior to developing data mining technologies. However, when the number of community members is sufficiently small and the heterogeneity of the expected value of knowledge among community members is sufficiently large, developing data mining technologies should be considered more important than the other if most community members are low-type ones. On the other hand, based on a screening technique, we find that the benefit of knowledge sharing in the incomplete information setting can be the same as that in the complete information setting if the cost of more efficient community member is smaller than that of less efficient one.     

Consolidating or non-consolidating queues: A game theoretic queueing model with holding costs

We consider a two-server queueing system in which the servers choose their service rate based on the demand and holding cost allocation scheme offered by the demand generating entity. We provide an optimal holding cost allocation scheme that leads to the maximum possible service rate for each of a pooled and a split system. Our results suggest that careful allocation of holding costs can create incentives that enable minimum turnaround times using a common queue.     

A fuzzy set theoretic interpretation of economic control limits

It has been the practice in industry that product specification limits have been used to judge between ‘good’ and ‘bad’ product. It is generally assumed that a given unit of product either does or does not conform to specifications. Traditional acceptance control charts have contributed to this notion. The present paper suggests that situations exist where a concept of graded conformance might provide a more accurate representation of reality. It exploits the theory of fuzzy sets to demonstrate how acceptance control charts can be constructed to explicitly account for the degree of conformance exhibited by each unit or sample of product.     

Developments in differential game theory and numerical methods: economic and management applications

This paper argues that the literature applying differential games in economics and management science has aimed to a large extent for analytical results. One reason is that the latter are usually seen as general, in the sense that they do not rely on specific values of the model’s parameters. However, they come at the cost of restricting the choice of the model to the class of so-called tractable differential games. Our aim is to discuss briefly the tools available for obtaining analytical results and to give an account of a number of (recent and earlier) developments in DG that, by and large, have not been used in these fields. Research supported by NSERC, Canada.     

Parental care as a differential game: A dynamic extension of the Houston–Davies game

An interpretation of the conflict between male and female parents during the process of caring for their common offspring by means of Game Theory was given in Houston and Davies. [A.I. Houston, N.B. Davies, The evolution of cooperation and life history in the dunnock Prunella modularis, in: R.M. Sibly, R.H. Smith (Eds.), Behavioral Ecology, Blackwell Scientific Publications, 1985, pp. 471–487]. Mathematically, this model represents a static game with continuous strategy sets. Recently, this model was reconsidered in a dynamic discrete time framework which also included state dependencies [J.M. McNamara et al., A dynamic game-theoretic model of parental care, J. Theor. Biol. 205 (2000) 605–623]. In this article, we give an interpretation of the parental care conflict in continuous time by means of a differential game with state dependent strategies.     

A game theoretic approach to option valuation under Markovian regime-switching models

In this paper, we consider a game theoretic approach to option valuation under Markovian regime-switching models, namely, a Markovian regime-switching geometric Brownian motion (GBM) and a Markovian regime-switching jump-diffusion model. In particular, we consider a stochastic differential game with two players, namely, the representative agent and the market. The representative agent has a power utility function and the market is a “fictitious” player of the game. We also explore and strengthen the connection between an equivalent martingale measure for option valuation selected by an equilibrium state of the stochastic differential game and that arising from a regime switching version of the Esscher transform. When the stock price process is governed by a Markovian regime-switching GBM, the pricing measures chosen by the two approaches coincide. When the stock price process is governed by a Markovian regime-switching jump-diffusion model, we identify the condition under which the pricing measures selected by the two approaches are identical.     

A survey of Germeier's game theory

Translated from Programmnoe Oborudovanie i Voprosy Prinyatiya Reshenii, pp. 201–210, 1989.     

A game theoretic model for two types of customers competing for service

Two types of customers arrive at a single server station and demand service. If a customer finds the server busy upon arrival (or retrial) he immediately departs and conducts a retrial after an exponential period of time and persists this way until he gets served. Both types of customers face linear costs for waiting and conducting retrials and wish to find optimal retrial rates which will minimize these costs. This problem is analysed as a two-person nonzero sum game. Both noncooperative strategies are studied.     

Dynamic resource allocation in fuzzy coalitions: a game theoretic model

We introduce an efficient and dynamic resource allocation mechanism within the framework of a cooperative game with fuzzy coalitions (cooperative fuzzy game). A fuzzy coalition in a resource allocation problem can be so defined that membership grades of the players in it are proportional to the fractions of their total resources. We call any distribution of the resources possessed by the players, among a prescribed number of coalitions, a fuzzy coalition structure and every membership grade (equivalently fraction of the total resources), a resource investment. It is shown that this resource investment is influenced by the satisfaction of the players in regard to better performance under a cooperative setup. Our model is based on the real life situations, where possibly one or more players compromise on their resource investments in order to help forming coalitions.     

Heterogeneous surface-to-air missile defense battery location: a game theoretic approach

In the context of an air defense missile-and-interceptor engagement, a challenge for the defender is that surface-to-air missile batteries often must be located to protect high-value targets dispersed over a vast area, subject to which an attacker may observe the disposition of batteries and subsequently develop and implement an attack plan. To model this scenario, we formulate a two-player, extensive form, three-stage, perfect information, zero-sum game that accounts for, respectively, a defender’s location of batteries, an attacker’s launch of missiles against targets, and a defender’s assignment of interceptor missiles from batteries to incoming attacker missiles. The resulting trilevel math programming formulation cannot be solved via direct optimization, and it is not suitable to solve via full enumeration for realistically-sized instances. We instead adapt the game tree search technique Double Oracle, within which we embed either of two alternative heuristics to solve an important subproblem for the attacker. We test and compare these solution methods to solve a designed set of 52 instances having parametric variations, from which we derive insights regarding the nature of the underlying problem. Enhancing the solution methods with alternative initialization strategies, our superlative methodology attains the optimal solution for over 75% of the instances tested and solutions within 3% of optimal, on average, for the remaining 25% of the instances, and it is promising for realistically-sized instances, scaling well with regard to computational effort.     

Comparing reinforcement learning approaches for solving game theoretic models: a dynamic airline pricing game example

Games can be easy to construct but difficult to solve due to current methods available for finding the Nash Equilibrium. This issue is one of many that face modern game theorists and those analysts that need to model situations with multiple decision-makers. This paper explores the use of reinforcement learning, a standard artificial intelligence technique, as a means to solve a simple dynamic airline pricing game. Three different reinforcement learning approaches are compared: SARSA, Q-learning and Monte Carlo Learning. The pricing game solution is surprisingly sophisticated given the game's simplicity and this sophistication is reflected in the learning results. The paper also discusses extra analytical benefit obtained from applying reinforcement learning to these types of problems.     

Analysis and design of selection committees: a game theoretic secretary problem

Firms often delegate important decisions to committees which are set up specifically for that purpose; for example selection committees. We analyze the equilibrium behavior of a game in which committee members (the players) interview candidates sequentially, either hiring or going on to the next one. The players have differing evaluations of candidates (e.g. one cares about typing skills; the other about IT skills), which become their utilities if the candidate is hired. We then consider the optimal design (rules of the game) of such a committee, from the point of view of the firm. That is, which rules hire candidates which maximize the firm’s utility. Our committee game has a first round in which the members sequentially, by order of player number, say ‘yea’ or ‘nea’ to the candidate. If there are sufficient ‘yeas’ then she is tentatively hired; otherwise she is rejected. In the former case, members who said nea can veto the candidate in the second round. Thus the candidate is either hired, rejected, or vetoed. In the last case, the member casting a veto has one less to use on later candidates. We analyze equilibria where a player may say ‘yea’ to a candidate he would prefer not to hire, in order to force the other player to use up a valuable veto. We show that for the uniform candidate distribution there is a unique equilibrium and better candidates for the firm are hired when there are more vetoes. However we exhibit a candidate distribution where increasing the numbers of vetoes results in hiring worse candidates.     

A cost-sharing method for an economic lot-sizing game

We present a cost-sharing method that is competitive, cross-monotonic and approximate cost recovering for an economic lot-sizing game under a weak triangle inequality assumption, along with numerical results showing the effectiveness of the proposed method.     

A simplified game model of the interaction between two countries

The mathematical model considered in the paper studies the interaction between the economies of two, generally unfriendly, countries with allowance for a sufficient preventive safety potential developed by one of the countries.