Non-cooperative matching games

Consider a market in which two distinct groups of agents face each other. Every agent can improve upon his status quo if he is matched with a member of the opposite group and if he agrees with his partner how to split the realized gain. The paper presents two non-cooperative games in which the agents construct the allocation without the help of an auctioneer. In the first game the set of equilibria coincides with the cooperative “stable solutions” which are well-established in this context. In the second game it is shown that a change of the order of the moves is sufficient to arrive at a unique equilibrium payoff.     

Bargaining in endogenous trading networks

We study a model in which heterogeneous agents first form a trading network where linking costs are positive but infinitesimally small. Then, a seller and a buyer are randomly selected among the agents to bargain through a chain of intermediaries. We determine both the trading path and the allocation of the surplus among the seller, the buyer and the intermediaries at equilibrium. We show that, under the initiator bargaining protocol, a trading network is pairwise stable if it is a core–periphery network where the core consists of all impatient agents who are linked to each other and the periphery consists of all patient agents who have a single link towards an impatient agent. Once agents do not know the impatience of other agents, each bilateral bargaining session may involve delay. Then, core–periphery networks may not be pairwise stable because agents may prefer to add links for reducing the length of trading paths and so avoiding costly delays in reaching a global agreement.     

A game theory approach in seller–buyer supply chain

In this paper, several seller–buyer supply chain models are proposed which incorporate both cost factors as well as elements of competition and cooperation between seller and buyer. We assume that unit marketing expenditure and unit price charged by the buyer influence the demand of the product being sold. The relationships between seller and buyer will be modeled by non-cooperative and cooperative games, respectively. The non-cooperative game is based on the Stackelberg strategy solution concept, where we consider separately the case when the seller is the leader (Seller-Stackelberg) and also when the buyer is the leader (Buyer-Stackelberg). Pareto efficient solutions will be provided for the cooperative game model. Numerical examples presented in this paper, including sensitivity analysis of some key parameters, will compare the results between different models considered.     

Assignment markets that are uniquely determined by their core

A matrix A defines an assignment market, where each row represents a buyer and each column a seller. If buyer i is matched with seller j, the market produces a_ij units of utility. Quint (1991) points out that usually many different assignment matrices exist that define markets with the same core and poses the question of when the matrix is uniquely determined by the core of the related market. We characterize these matrices in terms of a strong form of the doubly dominant diagonal property. A matching between buyers and sellers is optimal if it produces the maximum units of utility. Our characterization allows us to show that the number of optimal matchings in markets uniquely characterized by their core is a power of two.     

The valuation of options on capacity with cost and demand uncertainty

Options contracts can provide trading partners with enhanced flexibility to respond to uncertain market conditions and allow for superior capacity planning thanks to early information on future demand. We develop an analytical framework to value options on capacity for production of non-storable goods or dated services. The market consists of a sequence of contract and spot market. Reservations are made during the contract market session in period 0, where the buyer’s future demand, the seller’s future marginal costs as well as the future spot price are uncertain, the latter being impacted neither by the buyer nor the seller. During the spot market session in period 1, the buyer may execute his options or satisfy his entire or additional demand from a competing seller in the spot market. The seller allocates reserved capacity now being called and attempts to sell remaining capacity into the spot market. Analytical expressions for the buyer’s optimal reservation quantity and the seller’s tariff are derived, making explicit the risk-sharing benefits of options contracts. The combination of an options contract and a spot market is demonstrated to be Pareto improving as compared to alternative market schemes. An analysis of the determinants of the efficiency gain characterizes industries particularly suitable to the options approach.     

Buyer behavior adaptation based on a fuzzy logic controller and prediction techniques

The current form of Web provides numerous product resources available to users. Users can rely on intelligent agents for purchase actions. These actions are taken in specific environments such as Electronic Markets (EMs). In this paper, we study the interaction process between buyers and sellers and focus on the buyer side. Each buyer has the opportunity to interact with a number of sellers trying to buy the most appropriate products. This interaction can be modeled as a finite horizon Bargaining Game (BG). In this game, players have opposite goals concerning the product price. We adopt a number of techniques in the buyer side trying to give the appropriate level of efficiency in the buyer decision process. The buyer uses a prediction mechanism in combination with the use of Fuzzy Logic (FL) theory in order to be able to predict the upcoming seller proposal and, thus, understand the seller pricing policy. Based on this, he/she can adapt his/her behavior when trying to purchase products. The buyer adaptation mechanism produces the belief that the buyer has about the seller pricing policy and a parameter that indicates his/her own pricing policy which yields the buyer offers in the upcoming rounds. Moreover, the buyer is based on FL system that derives the appropriate actions at every round of the BG. Our results show that the combination of Fuzzy Logic (FL) with the above-mentioned techniques provides an efficient decision mechanism in the buyer side that in specific scenarios outperforms an optimal stopping model.     

Price oligopoly as a cooperative game

We consider an oligopolistic market as follows. In the market, one good is traded for money. Each oligopolist is a price setter and has the same linear cost function. Each buyer is a price taker and buys the good from oligopolists setting the lowest price. We formulate this market as a cooperative game, and consider two kinds of solution concepts, the core and a bargaining set of the game. First we show that in the monopolistic market, the core gives the monopoly price, but in the oligopolistic market, the core is empty. Second, we obtain the bargaining set of the oligopolistic market.     

中介企业的服务定价研究

定价问题是中介企业的核心问题之一。本主要目的是探讨中介企业如何对自己提供的中介服务进行定价。定性研究表明：中介对买卖双方收取的服务费用与以下三个因素有关1．双方在选择中介交易方式下节约的交易成本；2．中介企业自身的成本；3．买卖双方面临的风险成本。并在此基础上，给出了中介企业定价的基本模型。     

On coalition formation: a game-theoretical approach

This paper deals with the question of coalition formation inn-person cooperative games. Two abstract game models of coalition formation are proposed. We then study the core and the dynamic solution of these abstract games. These models assume that there is a rule governing the allocation of payoffs to each player in each coalition structure called a payoff solution concept. The predictions of these models are characterized for the special case of games with side payments using various payoff solution concepts such as the individually rational payoffs, the core, the Shapley value and the bargaining set M₁ ⁽ⁱ⁾. Some modifications of these models are also discussed.     

Manipulation via endowments in auctions with multiple goods

We study manipulation via endowments in a market in an auction setting with multiple goods. In the market, there are buyers whose valuations are their private information, and a seller whose set of endowments is her private information. A social planner, who wants to implement a socially desirable allocation, faces the seller’s manipulation via endowments, in addition to buyers’ manipulation of misreporting their valuations. We call a mechanism immune to the seller’s manipulation via endowments destruction-proof. In general, there exists no mechanism which is destruction-proof, together with strategy-proofness of the buyers, efficiency, and participation. Nevertheless, we find a restricted domain of the buyers’ valuation profiles satisfying a new condition called per-capita goods–buyer submodularity. We show that, in this domain, there exists a mechanism which is destruction-proof, together with the above properties. The restriction is likely to be met when each winner’s valuation is close to the next-highest valuation. We also provide a relation to monopoly theory, and argue that per-capita goods–buyer submodularity is independent of the standard elasticity argument.     

Prevention efforts,insurance demand and price incentives under coherent risk measures

This paper studies an equilibrium model between an insurance buyer and an insurance seller, where both parties’ risk preferences are given by convex risk measures. The interaction is modeled through a Stackelberg type game, where the insurance seller plays first by offering prices, in the form of safety loadings. Then the insurance buyer chooses his optimal proportional insurance share and his optimal prevention effort in order to minimize his risk measure. The loss distribution is given by a family of stochastically ordered probability measures, indexed by the prevention effort. We give special attention to the problems of self-insurance and self-protection, and show that if the buyer’s risk measure decreases faster in effort than his expected loss, optimal effort is non-decreasing in the safety loading with a potential discontinuity when optimal coverage switches from full to zero. On the contrary, if the decrease of the buyer’s risk measure is slower than the expected loss, optimal effort may or may not be non-decreasing in the safety loading. In case of Pareto distributed losses, the seller sets the highest possible price under which the buyer still prefers full insurance over no insurance. We also analyze the case of discrete distributions: on the one hand, for self-protection, under the assumption that the marginal impact of the effort is higher on small losses than it is on catastrophic losses, the optimal effort is non-decreasing in the safety loading. On the other hand, in the case of self-protection, more conditions are needed, in particular, we obtain sufficient conditions for the optimal effort to be non-decreasing or non-monotone in the safety loading.     

An axiomatic approach to egalitarianism in TU-games

A core concept is a solution concept on the class of balanced games that exclusively selects core allocations. We show that every continuous core concept that satisfies both the equal treatment property and a new property called independence of irrelevant core allocations (IIC) necessarily selects egalitarian allocations. IIC requires that, if the core concept selects a certain core allocation for a given game, and this allocation is still a core allocation for a new game with a core that is contained in the core of the first game, then the core concept also chooses this allocation as the solution to the new game. When we replace the continuity requirement by a weak version of additivity we obtain an axiomatization of the egalitarian solution concept that assigns to each balanced game the core allocation minimizing the Euclidean distance to the equal share allocation.     

Noncooperative selection of the core

For bargaining environments given by transferable utility characteristic functions that are zero-normalized and admit a nonempty core, we find a class of random-proposer bargaining games, generalized from Okada (1993), such that there is a one-to-one mapping from these games to the core, each game realizes the corresponding core allocation as its unique (ex ante) Stationary Subgame Perfect Equilibrium (SSPE) payoff profile, and every ex post SSPE payoff profile converges to the core allocation as the discount factor goes to one. The result has a natural interpretation in terms of bargaining power. Received: December 2000/Revised: August 2002     

Convex and exact games with non-transferable utility

We generalize exactness to games with non-transferable utility (NTU). A game is exact if for each coalition there is a core allocation on the boundary of its payoff set.     

Seller—buyer System Co-operation in a Monopolistic Market

This paper deals with a situation in which the buyer is in a monopolistic position with respect to the seller, and examines the issues and advantages of co-operation in a seller–buyer inventory control system. Game theory concepts form the foundation for the analysis of these issues. Initially, the relationship between the seller and the buyer is modelled as a non-cooperative two-stage game, and it is noted that the traditional EOQ formula is one of the results. Then, interactive game theory is utilized to address the problem of system co-operation as well as to determine optimal system order quantity-pricing strategies. Mutual incentives and motivations for system co-operation are also discussed. Among several alternative methods, the combination of an equal profit sharing role implemented via quantity discounting is demonstrated as the best mechanism for achieving system co-operation. Finally, the similarities and differences between the proposed model and those in the literature are discussed.     

重复n人随机合作对策的核心

以Su ijs等人(1995)引入的随机合作对策的模型为基础,建立了重复n人随机合作对策的理论,定义了重复n人随机合作对策的支付序列以及支付序列的优超关系,并由此给出了重复n人随机合作对策的核心、超可加性和凸性的定义,并讨论了该核心的一些特征和性质.     

A two-stage supply chain coordination mechanism considering price sensitive demand and quantity discounts

This paper explores the coordination between a supplier and a buyer within a decentralized supply chain, through the use of quantity discounts in a game theoretic model. Within this model, the players face inventory and pricing decisions. We propose both cooperative and non-cooperative approaches considering that the product traded experiences a price sensitive demand. In the first case, we study the dynamics of the game from the supplier's side as the leader in the negotiation obtaining a Stackelberg equilibrium, and then show how the payoff of this player could still improve from this point. In the second case, a cooperative model is formulated, where decisions are taken simultaneously, emulating a centralized firm, showing the benefits of the cooperation between the players. We further formulate a pricing game, where the buyer is allowed to set different prices to the final customer as a reaction to the supplier's discount decisions. For the latter we investigate the difference between feasibility of implementing a retail discount given a current coordination mechanism and without it. Finally the implications of transportation costs are analyzed in the quantity discount schedule. Our findings are illustrated with a numerical example showing the difference in the players’ payoff in each case and the optimal strategies, comparing in each case our results with existing work.     

The asymptotic core,nucleolus and Shapley value of smooth market games with symmetric large players

We examine the asymptotic nucleolus of a smooth and symmetric oligopoly with an atomless sector in a transferable utility (TU) market game. We provide sufficient conditions for the asymptotic core and the nucleolus to coincide with the unique TU competitive payoff distribution. This equivalence results from nucleolus of a finite TU market game belonging to its core, the core equivalence in a symmetric oligopoly with identical atoms and single-valuedness of the core in the limiting smooth game. In some cases (but not always), the asymptotic Shapley value is more favourable for the large traders than the nucleolus, in contrast to the monopoly case (Einy et al. in J Econ Theory 89(2):186–206, 1999), where the nucleolus allocation is larger than the Shapley value for the atom.     

A comparison of the alpha‐ and beta‐characteristic functions in cooperative non‐sidepayment n‐person games 1

This article reports a test of theories of payoff allocation in n‐person game‐theoretic systems. An experimental study was conducted to test the relative predictive accuracy of three solution concepts (imputation set, stable set, core) in the context of 4‐person, 2‐strategy non‐sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both α‐effectiveness (von Neumann‐Morgenstern) and β‐effectiveness (Aumann), making a total of six predictive theories under test. Two important results emerged. First, the data show that the g‐imputation set was more accurate than the a‐imputation set, the β‐stable set was more accurate than the α‐stable set, and the (3‐core was more accurate than the α‐core; in other words, for each of the solutions tested, the prediction from any solution concept based on (β‐effectiveness was more accurate than the prediction from the same solution based on a‐effectiveness. Second, the β‐core was the most accurate of the six theories tested. Results are interpreted as showing that β‐effectiveness is superior to a‐effectiveness as a basis for payoff predictions in cooperative non‐sidepayment games.     

Stability property of matchings is a natural solution concept in coalitional market games

Stability of matchings was proved to be a new cooperative equilibrium concept in Sotomayor (Dynamics and equilibrium: essays in honor to D. Gale, 1992). That paper introduces the innovation of treating as multi-dimensional the payoff of a player with a quota greater than one. This is done for the many-to-many matching model with additively separable utilities, for which the stability concept is defined. It is then proved, via linear programming, that the set of stable outcomes is nonempty and it may be strictly bigger than the set of dual solutions and strictly smaller than the core. The present paper defines a general concept of stability and shows that this concept is a natural solution concept, stronger than the core concept, for a much more general coalitional game than a matching game. Instead of mutual agreements inside partnerships, the players are allowed to make collective agreements inside coalitions of any size and to distribute his labor among them. A collective agreement determines the level of labor at which the coalition operates and the division, among its members, of the income generated by the coalition. An allocation specifies a set of collective agreements for each player.