Patent-investment games under asymmetric information

This paper analyzes preemptive patenting in a two-stage real options game where an incumbent firm competes with a potential entrant firm for the patent of a substitute product in a product market with profit flow uncertainty. The incumbent suffers loss of monopoly in the product market if the entrant acquires the patent of a substitute product and later commercializes the product. Our patent-investment game model assumes that the entrant has complete information on the incumbent’s commercialization cost while the incumbent only knows the distribution of the entrant’s cost. We investigate the impact of information asymmetry on the preemption strategies adopted by the two competing firms on patenting the substitute product by comparing the optimal preemption strategies and the real option value functions of the two competing firms under complete information and information asymmetry. Our analysis reveals that the informationally disadvantaged incumbent always suffers from loss in its real option value of investment since it tends to act more aggressively in competing for the patent. On the other hand, the real option value of investment of the informationally advantaged entrant may be undermined or enhanced. The incumbent’s aggressive response under information asymmetry may lead to reversal of winner in the patent race. We also examine how information asymmetry may affect the occurrence of sleeping patent and the corresponding expected duration between the two stages of patenting and product commercialization.     

Resource Dynamics under Partial Cooperation in an Oligopoly

We study the long-run evolution of a renewable resource which is subject to harvest by partially cooperating players who sell the harvested quantities on distinct markets. We derive explicit expressions for the total harvesting quantity of all players in this general framework and investigate the dependence of the total and relative harvest rates on the level of cooperation, available fish stock, and fishing costs. Combining the biological growth model with oligopoly leads to a nonlinear dynamic law for the evolution of the fish stock in the presence of commercial fishing. We provide also existence results for its equilibrium and examine the asymptotic behavior of the equilibrium. We are grateful for the critical comments and suggestions of three anonymous referees.     

Competition through capacity investment under asymmetric existing capacities and costs

This paper discusses the way that different operational characteristics including existing capacity, scale economies, and production policy have an important influence on the capacity outcomes when firms compete in the market place. We formulate a game-theoretical model where each firm has an existing capacity and faces both fixed and variable costs in purchasing additional capacity. Specifically, the firms simultaneously (or sequentially) make their expansion decisions, and then simultaneously decide their production decisions with these outputs being capacity constrained. We also compare our results with cases where production has to match capacity. By characterizing the firms’ capacity and production choices in equilibrium, our analysis shows that the operational factors play a crucial role in determining what happens. The modeling and analysis in the paper gives insight into the way that the ability to use less production capacity than has been built will undermine the commitment value of existing capacity. If a commitment to full production is not possible, sinking operational costs can enable a firm to keep some preemptive advantage. We also show that the existence of fixed costs can introduce cases where there are either no pure strategy equilibrium or multiple equilibria. The managerial implications of our analysis are noted in the discussion. Our central contribution in this paper is the innovative integration of the strategic analysis of capacity expansion and well-known (s,S)$(s\text{,}S)$ policy in operations and supply chain theory.     

Weak acyclic coloring and asymmetric coloring games

We introduce the notion of weak acyclic coloring of a graph. This is a relaxation of the usual notion of acyclic coloring which is often sufficient for applications. We then use this concept to analyze the (a,b)-coloring game. This game is played on a finite graph G, using a set of colors X, by two players Alice and Bob with Alice playing first. On each turn Alice (Bob) chooses a (b) uncolored vertices and properly colors them with colors from X. Alice wins if the players eventually create a proper coloring of G; otherwise Bob wins when one of the players has no legal move. The (a,b)-game chromatic number of G, denoted (a,b)-χ_g(G), is the least integer t such that Alice has a winning strategy when the game is played on G using t colors. We show that if the weak acyclic chromatic number of G is at most k then (2,1)-.     

Transshipment games with identical newsvendors and cooperation costs

In a transshipment game, supply chain agents cooperate to transship surplus products. Although the game has been well studied in the OR literature, the fundamental question whether the agents can afford cooperation costs to set up and maintain the game in the first place has not been addressed thus far. This paper addresses this question for the cooperative transshipment games with identical agents having normally distributed independent demands. We provide characterization of equal allocations which are in the core of symmetric games, and prove that not all transshipment games are convex. In particular, we prove that though individual allocations grow with the coalition size, the growth diminishes according to two rules of diminishing individual allocations. These results are the basis for studying the games with cooperation costs. We model the cooperation costs by the cooperation network topology and the cooperation cost per network link. We consider two network topologies, the clique and the hub, and prove bounds for the cost per link that render coalitions stable. These bounds always limit coalition size for cliques. However, the opposite is shown for hubs, namely newsvendors can afford cooperation costs only if their coalition is sufficiently large.     

Control costs and potential functions for spatial games

Van Damme and Weibull (1998, 2002) model the noise in games as endogenously determined tremble probabilities, by assuming that with some effort players can control the probability of implementing the intended strategy. Following their methodology, we derive logit-like adjustment rules for games played on quasi-symmetric weighted graphs and explore the properties of the ensuing Markov chain. Received: November 2000/Revised: June 2002     

On the asymptotic convergence to mixed equilibria in 2×2 asymmetric games

We analyse the stability properties of mixed equilibria in 2×2 asymmetric games under evolutionary dynamics. With the standard replicator dynamics these equilibria are stable but not asymptotically stable. We modified the replicator dynamics by introducing players of two types: myopies — like in the standard replicator dynamics — and best responders. The behaviour of the latter is described by a continuos time version of the best reply dynamics. Asymptotic convergence under theModified Replicator Dynamics is proved by identifying a strictly decreasing Ljapunov function. We argue that the finding has important implications to justify the use of economic models with mixed strategy equilibria.     

Approximate cores of replica games and economies: Part II: Set-up costs and firm formation in coalition production economies

A model of a coalition production economy allowing set-up costs, indivisibilities,and nonconvexities is developed. It is shown that for all sufficiently large replications, approximate cores of the economy are nonempty.     

A strategic r&d planning model with an application to an energy research organization

This paper describes a two-stage strategic planning model for determining the optimal R&D portfolio in the presence of both exploratory and developmental research projects. An example is illustrated in the context of energy research. Research portfolios are analysed using a Bayesian approach in which probability assessments are updated as new information generated by exploratory research becomes available. Useful insights are obtained through sensitivity analysis. It is found that exploratory research tends to exhibit a lumpy characteristic.     

Replenishment decisions under an all-units discount schedule and stepwise freight costs

In this study, we analyze the replenishment decisions under a general replenishment cost structure that includes stepwise freight costs and all-units quantity discounts. We first formulate a general model that accounts for a larger class of problems and prove several useful properties of the expected profit function. We later utilize these properties to develop a computational solution approach to find the optimal order quantity. As an application of the general results, we study the replenishment decisions in the single-period, i.e., the Newsboy, problem considering several scenarios that model the cost considerations either for the buyer or for both the buyer and the vendor.     

The theory of energy for sub-Laplacians with an application to quasi-continuity

In this paper, we provide a suitable theory for the energy where μ is a Radon measure and Γ is the fundamental solution of a sub-Laplacian on a stratified group As a significant application, we prove the quasi-continuity of superharmonic functions related to . The proofs are elementary and mostly rely on the use of appropriate mean-value formulas and mean-integral operators relevant to the Potential Theory for .     

On computational complexity of membership test in flow games and linear production games

Let Γ≡(N,v) be a cooperative game with the player set N and characteristic function v: 2^N→R. An imputation of the game is in the core if no subset of players could gain advantage by splitting from the grand coalition of all players. It is well known that, for the flow game (and equivalently, for the linear production game), the core is always non-empty and a solution in the core can be found in polynomial time. In this paper, we show that, given an imputation x, it is NP-complete to decide x is not a member of the core, for the flow game. And because of the specific reduction we constructed, the result also holds for the linear production game. Received: October 2000/Final version: March 2002     

Robust energy planning in buildings with energy and comfort costs

Energy management in buildings is addressed in this paper. The energetic impact of buildings in the current energetic context is first depicted. Then the studied optimization problem is defined as the optimal management of production and consumption activities in houses. A scheduling problem is identified to adjust the energy consumption to both the energy cost and the inhabitant’s comfort. The available flexibilities of the services provided by domestic appliances are used to compute optimal energy plans. These flexibilities are associated to time windows or heating storage abilities. A constraints formulation of the energy allocation problem is given. A derived mixed linear program is used to solve this problem. The energy consumption in houses is very dependent to uncertain data such as weather forecasts and inhabitants’ activities. Parametric uncertainties are introduced in the home energy management problem in order to provide robust energy allocation. Robust linear programming is implemented. Event related uncertainties are also addressed through stochastic programming in order to take into account the inhabitant’s activities. A scenario based approach is implemented to face this robust optimization problem.     

Repeated games with asymmetric information and random price fluctuations at finance markets

This paper is concerned with multistage bidding models introduced in De Meyer and Moussa Saley (Int J Game Theory 31:285–319, 2002) to analyze the evolution of the price system at finance markets with asymmetric information. The repeated games are considered modelling the biddings with the admissible bids k/m, unlike the above mentioned paper, where arbitrary bids are allowed. It is shown that the sequence of values of n-step games is bounded from above and converges to the value of the game with infinite number of steps. The optimal strategies of infinite game generate a symmetric random walk of transaction prices over admissible bids with absorbing extreme points. The value of infinite game is equal to the expected duration of this random walk multiplied by the constant one-step gain of informed Player 1. This study was supported by the grant 04-06-80430 of Russian Foundation of Basic Research which is gratefully acknowledged. I am thankful to anonymous referees and to William Thomson for instructive and helpful remarks and comments.     

Zero-sum stochastic games with unbounded costs: Discounted and average cost cases

Zero-sum stochastic games with countable state space and with finitely many moves available to each player in a given state are treated. As a function of the current state and the moves chosen, player I incurs a nonnegative cost and player II receives this as a reward. For both the discounted and average cost cases, assumptions are given for the game to have a finite value and for the existence of an optimal randomized stationary strategy pair. In the average cost case, the assumptions generalize those given in Sennott (1993) for the case of a Markov decision chain. Theorems of Hoffman and Karp (1966) and Nowak (1992) are obtained as corollaries. Sufficient conditions are given for the assumptions to hold. A flow control example illustrates the results.     

Nonzero-sum stochastic games with unbounded costs: Discounted and average cost cases

We treat non-cooperative stochastic games with countable state space and with finitely many players each having finitely many moves available in a given state. As a function of the current state and move vector, each player incurs a nonnegative cost. Assumptions are given for the expected discounted cost game to have a Nash equilibrium randomized stationary strategy. These conditions hold for bounded costs, thereby generalizing Parthasarathy (1973) and Federgruen (1978). Assumptions are given for the long-run average expected cost game to have a Nash equilibrium randomized stationary strategy, under which each player has constant average cost. A flow control example illustrates the results. This paper complements the treatment of the zero-sum case in Sennott (1993a).     

Lower and upper bounds for linear production games

We study the problem of allocating the total profit of a production enterprise among the resource owners, using the game-theoretic framework introduced by Owen [Owen, G., 1975. On the core of linear production games. Mathematical Programming 9, 358–370]. We provide lower (upper) bounds on the values of the game by aggregating over columns (rows) of the LP-problem. By choosing aggregation weights corresponding to optimal solutions of the primal (dual) LP-problem, we can create new games whose core form a superset (subset) of the original core. An estimate of the resulting error, in terms of an ?$?$-core, is obtained by solving a mixed integer programming problem, and we also suggest an iterative procedure for improving the bounds. Using a set of numerical examples, we investigate how the performance of the aggregation approach depends on the structure of the problem data.     

Network planning under uncertainty with an application to hydropower generation

Summary We present a general modeling framework for therobust optimization of linear network problems with uncertainty in the values of the right-hand side. In contrast to traditional approaches in mathematical programming, we use scenarios to characterize the uncertainty. Solutions are obtained for each scenario and these individual scenarios are aggregated to yield a nonanticipative or implementable policy that minimizes the regret of wrong decisions. A given solution is termed robust if it minimizes the sum over the scenarios of the weighted upper difference between the objective function value for the solution and the objective function value for the optimal solution for each scenario, while satisfying certain nonanticipativity constraints. This approach results in a huge model with a network submodel per scenario plus coupling constraints. Several decomposition approaches are considered, namely Dantzig-Wolfe decomposition, various types of Benders decomposition and different quadratic network approaches for approximating Augmented Lagrangian decomposition. We present computational results for these methods, including two implementation versions of the Lagrangian based method: a sequential implementation and a parallel implementation on a network of three workstations.