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.     

A duopolistic spatial competition model with non-zero conjectural variation

Consider a two-stage non-cooperative Cournot game with location choice involving two firms. There aren spatially separated markets located at the vertices of a network. Each firm, first selects the location of a facility and then selects the quantities to supply to the markets in order to maximize its profit. Non-zero conjectural variation at the second stage is studied. Equilibrium in the quantities offered by each firm in the markets exists. Furthermore, when the demand in each market is sufficiently large, each firm chooses to locate its facility at the vertices. Partially financed by FEDER and Ministerio de Ciencia y Tecnología, grant BFM2002-04525-C02-01, and Universidad de Las Palmas de Gran Canaria, grant UNI2004/12     

不确定性下强Berge均衡的存在性

在已知不确定参数变化的范围下,研究了非合作博弈与广义非合作博弈的强Berge均衡的存在性,基于强Berge均衡与不确定性下非合作博弈的强Nash均衡的概念,给出了不确定参数下非合作博弈与广义非合作博弈的强Berge均衡的定义,并利用Fan-Glicksberg不动点定理证明其存在性,最后用算例验证其可行性.     

Two-settlement electricity markets with price caps and Cournot generation firms

We compare two alternative mechanisms for capping prices in two-settlement electricity markets. With sufficient lead time, forward market prices are implicitly capped by competitive pressure of potential entry that will occur when forward prices rise above some backstop price. Another more direct approach is to cap spot prices through a regulatory intervention. In this paper we explore the implications of these two alternative mechanisms in a two-settlement Cournot equilibrium framework. We formulate the market equilibrium as a stochastic equilibrium problem with equilibrium constraints (EPEC) capturing congestion effects, probabilistic contingencies and horizontal market power. As an illustrative test case, we use the 53-bus Belgian electricity network with representative generator costs but hypothetical demand and ownership structure. Compared to a price-uncapped two-settlement system, a forward cap increases firms’ incentives for forward contracting, whereas a spot cap reduces such incentives. Moreover, in both cases, more forward contracts are committed as the generation resource ownership structure becomes more diversified.     

Can core allocations be achieved in avoidable fixed cost environments using two-part price competition?

Two environments are studied in which sellers have only avoidable fixed costs and fixed capacities: (a) in the first, the core exists and is supportable by a competitive equilibrium; (b) in the second, the core exists but there is no competitive equilibrium. In both cases, demand price is constant up to capacity. Experiments using the double auction institution fail to converge to 100% efficiency allocations in either environment. We study a new mechanism in which sellers each submit fixed vendor's fees, which must be paid before units can be sold, as well as a price and corresponding maximum quantity. Buyers submit price-quantity bids. A computing center determines allocations that maximize the aggregate surplus subject to the price, quantity, and vendor fee constraints. We report 20 experiments: 5 inexperienced (45 periods) and 5 experienced (75 periods) subject groups in each of the designs (a) and (b). Buyers are simulated to be fully revealing. The same four sellers participate in both inexperienced and experienced sessions. We explain why this environment proves difficult in these experiments and what we intend to do about it in further iterations.     

On coordination games with quantum correlations

A necessary condition is derived that helps to determine whether an entangled quantum system can improve coordination in a game with incomplete information. The author would like to express his gratitude to Diana Bloom for her help with editing this paper.     

On differential games with a feedback nash equilibrium

This note provides a lemma on differential games which possess a feedback Nash equilibrium (FNE). In particular, it shows that (i) a class of games with a degenerate FNE can be constructucted from every game which has a nondegenerate FNE and (ii) a class of games with a nondegenerate FNE can be constructed from every game which has a degenerate FNE.The author would like to thank an anonymous referee for invaluable comments and suggestions.     

Existence of minmax points in discontinuous strategic games

In this note we prove the existence of minmax points for strategic form games where the sets of strategies are topological spaces and the payoff functions satisfy conditions weaker than continuity. The employed tools are the class of transfer weakly upper continuous functions and the class of weakly lower pseudocontinuous functions. An example shows that our result is of minimal character.     

On the Probability of Existence of Pure Equilibria in Matrix Games

In a recent paper (Ref. 1), Papavassilopoulos obtained results on the probability of the existence of pure equilibrium solutions in stochastic matrix games. We report a similar result, but where the payoffs are drawn from a finite set of numbers N. In the limiting case, as N tends to infinity, our result and that of Papavassilopoulos are identical. We also cite similar results obtained independently by others, some of which were already independently brought to the notice of Papavassilopoulos by Li Calzi as reported in Papavassilopoulos (Ref. 2). We cite a much earlier result obtained by Goldman (Ref. 3). We also cite our related work (Ref. 4), in which we derive the conditions for the existence of mixed strategy equilibria in two-person zero-sum games.     

Sensitivity analysis of markup equilibria in complementary markets

We study the competitive structure of a market in which firms compete to provide various products within a bundle. Firms adopt price functions proportional to their per-unit costs by selecting markups. We consider two measures reflecting, respectively, the intensity of direct competition and the impact of complementarity on each producer’s markup. We characterize the sensitivity of these terms to various changes in the market structure and relate this to changes in producer profits and the social efficiency of the market.     

On nash equilibrium solutions in nonzero-sum stochastic games with complete information

Two-person nonzero-sum stochastic games with complete information are considered. It is shown that it is sufficient to search the equilibrium solutions in a class of deterministic strategy pairs — the so-calledintimidation strategy pairs. Furthermore, properties of the set of all equilibrium losses of such strategy pairs are proved.     

允许卖空的资本市场中存在非负均衡价格向量的充要条件

For the capital market satisfying standard assumptions that are widely adopted in the equilibrium analysis,a necessary and sufficient condition for the existence and uniqueness of a nonnegative equilibrium price vector that clears the mean-variance capital market with short sale allowed is derived. Moreover, the given explicit formula for the equilibrium price shows clearly the relationship between prices of assets and statistical properties of the rate of return on assets, the desired rates of return of individual investors as well as other economic quantities.The economic implication of the derived condition is briefly discussed. These results improve the available results about the equilibrium analysis of the mean-variance market.     

On competitiveness in uniform utility allocation markets

We call a market competitive if increasing the endowment of one buyer does not increase the equilibrium utility of another. We show that every competitive uniform utility allocation market is a submodular utility allocation market, answering a question of Jain and Vazirani [K. Jain, V.V. Vazirani, Eisenberg-Gale markets: Algorithms and structural properties, in: STOC, 2007]. Our proof proceeds via characterizing non-submodular fractionally sub-additive functions.     

Competitive facility location and design with reactions of competitors already in the market

A new retail facility is to locate and its service quality is to determine where similar facilities of competitors offering the same goods are already present. The market share captured by each facility depends on its distance to customers and its quality, which is described by a probabilistic Huff-like model. In order to maximize the profit of the new facility, a two-stage method is developed, which takes into account the reactions of the competitors. In the quality decision stage, the competitive decision process occurring among facilities is modelled as a game, whose solution is given by its Nash equilibrium. The solution, which can be represented as functions of the location of the new facility, is obtained by analytical resolution of a system of equations in the case of one facility in the market or by polynomial approximation in the case of multiple facilities. In the location decision stage, an interval based global optimization method is used to determine the best location of the new facility. Numerical experiments on randomly generated instances demonstrate the effectiveness of the method.     

On the stability of the solution for multiobjective generalized games with the payoffs perturbed

This paper studies the stability of weakly Pareto-Nash and Pareto-Nash equilibrium for multiobjective generalized games with the payoff perturbed. Using a simple characterization of the weakly Pareto-Nash solution, we obtain a generic continuous result concerning weakly Pareto-Nash solution mapping. Examples are given to show that Pareto-Nash equilibrium mapping is neither upper semicontinuous nor lower semicontinuous. Through seeking the sub-mapping, we prove that most multiobjective generalized games have at least one essential Pareto-Nash solution.     

On Cournot-Nash equilibria with exogenous uncertainty

A large body of literature has accumulated which examines how the optimal solution of an agent maximizing the expectation of a real-valued function, depending on a random parameterp and the agent's behaviorx, reacts to perturbations in the first and second moments ofp. Here, by an approximation valid for small uncertainty, we allow many agents and consider their behavior in a Cournot-Nash equilibrium. We also allowp to depend on the behaviors of the participating agents. We apply the analysis to two models, one of a Cournot oligopoly, the other of a cooperative of individuals where there is uncertainty in the return to communal work.The second and third authors are grateful to the British Council (Academic Links and Interchange Scheme) for financial support.     

Semi-Lagrangean approach for price discovery in markets with non-convexities

From standard economic theory, the market clearing price for a commodity is set where the demand and supply curves intersect. Convexity is a property that economic models require for a competitive equilibrium, which is efficient and well-behaved and provides equilibrium prices. However, some markets present non-convexities due to their cost structure or due to some operational constraints that need to be addressed. This is the case for electricity markets where the electricity producers incur costs for shutting down a generating unit and then bringing it back on. Non-convex cost structures can be a challenge for the price discovery process, since the supply and demand curves may not intersect, or if they intersect, the price found may not be high enough to cover the total cost of production. We apply a Semi-Lagrangean approach to find a price that can be applied in the electricity pool markets where a central system operator decides who produces and how much they should produce. By applying the model to an example from the literature, we found prices that are high enough to cover the producer’s total costs, and follows the optimal solution for achieving mining cost in production. The prices are an alternative solution to the price discovery problem in non-convexities economies; in addition, they provide nonnegative profits to all the generators without the use of side-payments or up-lifts, and closes the integrality gap.     

On the saddle-point stability for a class of dynamic games

In this paper, we study the stability properties of the class of capital accumulation games introduced by Fershtman and Muller (Ref. 1). Both discrete and continuous time versions are discussed. It is shown that the open-loop Nash equilibrium solutions for both games are characterized by a general saddle-point property, a result best known from the turnpike literature in optimal growth theory. In the case of zero discount rates, an even stronger result can be derived: As long as the Hessian matrix of the instantaneous profit functions has a quasidominant diagonal, no pure imaginary roots are possible.The authors thank J. Boyd III, G. Feichtinger, S. Jørgensen, and G. Schwann for helpful comments. The first author acknowledges financial support from the Natural Science and Engineering Research Council of Canada, Grant No. OGP-0037342.