Mechanism design for a multicommodity flow game in service network alliances

We study a collaborative multicommodity flow game where individual players own capacity on the edges of the network and share this capacity to deliver commodities. We present membership mechanisms, by adopting a rationality based approach using notions from game theory and inverse optimization, to allocate benefits among the players in such a game.     

Two different routes to complex dynamics in an heterogeneous triopoly game

We study a triopoly game with heterogeneous players. The market is characterized by a nonlinear (isoelastic) demand function and three competitors. The main novelty is the double route to complex dynamics that we find and is quite rare in heterogeneous triopoly models. We show that the two routes have important implications for the economic interpretation of the dynamics emerging when the Cournot–Nash equilibrium becomes locally unstable. Moreover the model displays multistability of different attractors, requiring a global analysis of the dynamical system.     

Educational effects in an experiment with the management game SINTO-Market

This paper examines how the educational background influences the performance of managers’ strategies. The research is based on data collected by an experiment with the management game SINTO-Market. This management game puts the players in a competitive situation in the branded food product sector, within which the subjects take over the role of the managers who have to find out the most successful strategy. From experimental research with this management game we will draw some interesting conclusions about human behavior in complex economic decision-making situations. To investigate educational effects the management game SINTO-Market was performed with students of different educational levels 17 times. The results show some significant differences between graduates and undergraduates.     

The Sprague-Grundy function of the game Euclid

We show that the Sprague-Grundy function of the game Euclid is given by g(x,y)=⌊|y/x-x/y|⌋ for x,y≥1.     

Atomic weights and the combinatorial game of bipass

We define an all-small ruleset, bipass, within the framework of normal play combinatorial games. A game is played on finite strips of black and white stones. Stones of different colors are swapped provided they do not bypass one of their own kind. We find a simple surjective function from the strips to integer atomic weights (Berlekamp, Conway and Guy 1982) that measures the number of units in all-small games. This result provides explicit winning strategies for many games, and in cases where it does not, it gives narrow bounds for the canonical form game values. We find game values for some parametrized families of games, including an infinite number of strips of value ?, and we prove that the game value ?2 does not appear as a disjunctive sum of bipass. Lastly, we define the notion of atomic weight tameness, and prove that optimal misére play bipass resembles optimal normal play.     

Comparative statics of a signaling game: An experimental study

In this paper a simple and basic signaling game is studied in an experimental environment. First, we check whether we can replicate some of the findings in the literature concerning equilibrium selection and the use and impact of costly signals. Second, and foremost, the comparative statics implications of the game are studied. The experimental results are related to the predictions of two competing behavioral models: a game model, in which subjects are assumed to behave in line with (refined) sequential equilibrium theory, and a decision model, in which subjects are assumed to behave as non-strategic decision makers. The experimental outcomes replicate the finding in the literature that costly messages are sent more frequently by ‘higher’ sender types (whose information is such that persuasion is also profitable to the responder), and that such messages have an impact on the behavior of the responder. These results are consistent with (versions of) both the game model and the decision model. The comparative statics results, however, clearly point in the direction of the decision model. Play is most strongly affected by ‘own’ payoff parameters, as predicted by the decision model, and less so by opponent's payoff parameters, as predicted by the mixed strategies of the refined sequential equilibrium. Particularly, a decision model in which players are assumed to adapt beliefs about opponents' choice probabilities in response to experience in previous play, appears to succeed best in organizing the data.     

Local minima of the trust region problem

We consider the minimization of a quadratic formzVz+2zq subject to the two-norm constraint z=. The problem received considerable attention in the literature, notably due to its applications to a class of trust region methods in nonlinear optimization. While the previous studies were concerned with just the global minimum of the problem, we investigate the existence of all local minima. The problem is approached via the dual Lagrangian, and the necessary and sufficient conditions for the existence of all local minima are derived. We also examine the suitability of the conventional numerical techniques used to solve the problem to a class of single-instruction multiple-data computers known as processor arrays (in our case, AMT DAP 610). Simultaneously, we introduce certain hardware-oriented multisection algorithms, showing their efficiency in the case of small to medium size problems.This research was partially supported by the National Physical Laboratories of England under Contract RTP2/155/127.     

Merit norms in the ultimatum game: an experimental study of the effect of merit on individual behavior and aggregate outcomes

Central European Journal of Operations Research - The paper reports the results of an ultimatum game experiment designed to test the effects of meritocratic norms on individual behavior and...     

A note on Buczolich's solution of the Weil gradient problem: a construction based on an infinite game

Summary Using an infinite game approach we reprove Buczolich's result that there exists a differentiable function f such that ∇f(0) = 0 and |∇ f |≧1 a.e.     

On the global convergence of trust region algorithms for unconstrained minimization

Many trust region algorithms for unconstrained minimization have excellent global convergence properties if their second derivative approximations are not too large [2]. We consider how large these approximations have to be, if they prevent convergence when the objective function is bounded below and continuously differentiable. Thus we obtain a useful convergence result in the case when there is a bound on the second derivative approximations that depends linearly on the iteration number.     

A polynomial expression for the Owen value in the maintenance cost game

The class of maintenance cost games was introduced in 2000 to deal with a cost allocation problem arising in the reorganization of the railway system in Europe. The main application of maintenance cost games regards the allocation of the maintenance costs of a facility among the agents using it. To that aim it was first proposed to utilize the Shapley value, whose computation for maintenance cost games can be made in polynomial time. In this paper, we propose to model this cost allocation problem as a maintenance cost game with a priori unions and to use the Owen value as a cost allocation rule. Although the computation of the Owen value has exponential complexity in general, we provide an expression for the Owen value of a maintenance cost game with cubic polynomial complexity. We finish the paper with an illustrative example using data taken from the literature of railways management.     

On the superlinear convergence of a trust region algorithm for nonsmooth optimization

It is proved that the second order correction trust region algorithm of Fletcher [5] ensures superlinear convergence if some mild conditions are satisfied.     

A differential game model of the marketing-operations interface

In the development of their dynamic strategies, the marketing and operations functions within a firm have differing objectives, and conflict between the two functions is common. The strategic interdependence involving marketing and operations decisions is modeled as a noncooperative differential game. Demand is assumed to be a function of price and advertising goodwill, and marketing controls price and advertising to maximize its discounted stream of revenue net of advertising costs. Backlogging is allowed, and operations controls production to minimize its discounted stream of production and backlog costs. A feedback Nash equilibrium is derived for the game, which allows a solution of the system of differential equations for goodwill and backlog, and is analyzed to study the nature of the dynamic strategies for price, advertising, and production.     

Scale changes and shared information in bargaining: An experimental study

This paper reports one of a series of experiments designed to test aspects of various game-theoretic models of bargaining. The results of this experiment consolidate those of previous experiments, which are first reviewed. The principal new result of this experiment is the observation, under conditions of partial information, of systematic violations of the axiom of independence of equivalent utility representations. The adequacy of various theories of bargaining to describe the observed data is also tested and discussed.     

Pure equilibria in a simple dynamic model of strategic market game

We present a discrete model of two-person constant-sum dynamic strategic market game. We show that for every value of discount factor the game with discounted rewards possesses a pure stationary strategy equilibrium. Optimal strategies have some useful properties, such as Lipschitz property and symmetry. We also show value of the game to be nondecreasing both in state and discount factor. Further, for some values of discount factor, exact form of optimal strategies is found. For β less than , there is an equilibrium such that players make large bids. For β close to 1, there is an equilibrium with small bids. Similar result is obtained for the long run average reward game.     

Monotonicity in the stock competition game with consumer search

Anupindi and Bassok investigate the impact of centralizing the stocks in a one-manufacturer-two-retailer supply chain with consumer search. They observed through numerical studies that in the decentralized scenario, the retailers’ order quantities are monotonic in the consumer search probability. This paper provides an analytical justification of this monotonicity.     

A procedure to compute the nucleolus of the assignment game

The assignment game introduced by Shapley and Shubik (1972)  [6] is a model for a two-sided market where there is an exchange of indivisible goods for money and buyers or sellers demand or supply exactly one unit of the goods. We give a procedure to compute the nucleolus of any assignment game, based on the distribution of equal amounts to the agents, until the game is reduced to fewer agents.     

Some remarks on the folk theorem in game theory

It is argued that although the pathological multiplicity of Nash equilibria of super games stated by the folk theorem can be removed by introducing limited observations into super games with a continuum of players, the consideration of super games in terms of the Nash equilibrium concept involves a more fundamental and conceptual difficulty.     

A dynamic Cournot–Nash game: a representation of a finitely repeated feedback game

This paper studies market outcome equivalence of two dynamic production-capital investment games under uncertainty. One is played under complete information, while the other, feedback (FB) game, is played under incomplete information about the opponents’ costs and market demand. The FB game structure may be observed in some newly initiated industries, in which a homogeneous good is exchanged via an auction mechanism. In that case, the FB game setting may predict the complete information equilibrium market outcomes.      

Competition under different reimbursement systems: The concept of an internet-based hospital management game

We have developed an internet-based management game to illustrate the economic and organisational decision-making process in a hospital by using discrete event simulation. Up to six hospitals compete against each other for inpatients with different disease categories and budget depending on hospital mission, regional health policy, inpatient reimbursement system (day-, case- and global-budget based) as well as labour and radiology technology market for 12 decision periods. Players can evaluate alternative actions for capacity planning as well as patient scheduling and control problems depending on different game situations. The uniqueness of COREmain hospital game consists of the internet-based framework, the combination of resource, process and financial result management, the competition of hospitals within a region and the consideration of different inpatient reimbursement systems. The deployment of this game in teaching, policy and research might improve policy making both at a hospital, regional and national level and also induce further research in these fields.