Intermediation in Search Markets

In markets, in which exchange requires costly search for trading partners, intermediaries can help to reduce the trading frictions. This intuition is modeled in a framework with heterogeneous agents, who have the choice between intermediated exchange and search accompanied by some bargaining procedure. The equilibria of such a game are characterized. In the case of a monopolistic intermediary, the tradeoff between the bid-ask spread and the costs of delay during private search determine the intermediary's clientele. In equilibrium the monopolist charges a positive spread. Traders with large gains from trade prefer to deal with him, whereas traders with relatively low gains from trade engage in search. In case of competition among intermediaries, the classical Bertrand result obtains, and bid and ask prices converge to the (unique) Walrasian equilibrium price. Thus, in the confines of the model, the Walrasian auctioneer of the market under consideration can be replaced by competing intermediaries. In addition a multiplicity of subgame perfect Nash equilibria emphasizes the coordination problems inherent in models of intermediation.     

Simple collective equilibria in stopping games

At each moment in time, an alternative from a finite set is selected by a stochastic process. Players observe the selected alternative and sequentially cast a yes or a no vote. If the set of players casting a yes vote is decisive for the selected alternative, it is accepted and the game ends. Otherwise the next period begins. We refer to this class of problems as stopping games. Collective choice games, quitting games, and coalition formation games are particular examples. When the core of a stopping game is non-empty, a subgame perfect equilibrium in pure stationary strategies is shown to exist. But in general, even subgame perfect equilibria in mixed stationary strategies may not exist. We show that aggregate voting behavior can be summarized by a collective strategy. We insist on pure strategies, allow for simple forms of punishment, and provide a constructive proof to show that so-called two-step simple collective equilibria always exist. This implies the existence of a pure strategy subgame perfect equilibrium. We apply our approach to the case with three alternatives exhibiting a Condorcet cycle and to a model of redistributive politics.     

An exact non-cooperative support for the sequential Raiffa solution

This article provides an exact non-cooperative foundation of the sequential Raiffa solution for two-person bargaining games. Based on an approximate foundation due to Myerson (1991) for any two-person bargaining game (S, d) an extensive form game G^S,d is defined that has an infinity of weakly subgame perfect equilibria whose payoff vectors coincide with that of the sequential Raiffa solution of (S, d). Moreover all those equilibria share the same equilibrium path consisting of proposing the Raiffa solution and accepting it in the first stage of the game.By a modification of G^S,d the analogous result is provided for subgame perfect equilibria. These results immediately extend to implementation of a sequential Raiffa (solution based) social choice rule in subgame perfect equilibrium.     

Implementation of the recursive core for partition function form games

In partition function form games, the recursive core (r-core) is implemented by a modified version of Perry and Reny’s [Perry, M., Reny, P., 1994. A non-cooperative view of coalition formation and the core. Econometrica 62, 795-817] non-cooperative game. Specifically, every stationary subgame perfect Nash equilibrium (SSPNE) outcome is an r-core outcome. With the additional assumption of total r-balancedness, every r-core outcome is an SSPNE outcome.     

A non-cooperative interpretation of bargaining sets

This paper provides a non-cooperative interpretation for bargaining sets concepts in economic environments. We investigate the implementability of the Aumann-Maschler and Mas-Colell bargaining sets, and provide mechanisms whose subgame perfect equilibrium outcomes realize these sets. These mechanisms, in contrast to general mechanisms suggested in the implementation literature, have a natural structure closely related to that of the rationale underlying the bargaining sets. Furthermore, the strategy sets consist mainly of allocations and coalitions (thus avoiding any reference to preference parameters) and are finite dimensional. Received: 17 February 1997 / Accepted: 2 February 1999     

Endogenous institutions in bureaucratic compliance games

We consider a set-up where two governments have either conflicting or matching preferences on the provision of differentiated (local) goods supplied by a common monopoly bureau. We develop a two-stage game. At stage-1, the two governments decide whether or not to merge into a single institution. At stage-2, all players simultaneously and independently take their decisions in terms of production and rents, with perfect knowledge of the other players' strategies. We solve the subgame perfect Nash equilibrium of this game, and show that, if the bureau immediately updates its objective function to institutional changes, then the governments always prefer merging. However, if there is an initial bureaucratic inertia in adjusting the bureau's objective function to the institutional change, then ruling politicians may prefer decentralisation to centralisation, depending on the strategic properties of the compliance game and on their own discounting. Received: May 1999 / Accepted April 2000     

Nash equilibria in a model of multiproduct price competition: an assignment problem

We study the market interaction of a finite number of single-product firms and a representative buyer, where the buyer consumes bundles of these goods. The buyers’ value function determines their willingness to pay for subsets of goods. We show that Nash-equilibrium outcomes are solutions of the linear relaxation of an integer programming assignment problem and that they always exist. The Nash-equilibrium price set is characterized by the Pareto frontier of the associated dual problem’s projection on the firms’ price vectors. We identify the Nash-equilibrium prices for monotonic buyers’ value functions and, more importantly, we show that some central solution concepts in cooperative game theory are (subgame perfect) equilibrium prices of our strategic game.     

Cournot outcomes under Bertrand–Edgeworth competition with demand uncertainty

We provide new results for two-stage games in which firms make capacity investments when demand is uncertain, then, when demand is realized, compete in prices. We consider games with demand rationing schemes ranging from efficient to proportional rationing. In all cases, there is a subgame perfect equilibrium outcome coinciding with the outcome of the Cournot game with demand uncertainty if and only if (i) the fluctuation in absolute market size is small relative to the cost of capacity, or (ii) uncertainty is such that with high probability the market demand is very large and with the remaining probability the market demand is extremely small. Otherwise, equilibria involve mixed strategies. Further, we show under efficient rationing that condition (i) is sufficient for the unique equilibrium outcome to be an equilibrium outcome of the Cournot game with demand uncertainty.     

Best response dynamics with level-n expectations in two-stage games

This paper analyzes behavior in repeatedly played two-stage games, where players choose actions in both stages according to best replies using level-n expectations about the opponent׳s actions in both stages. Level-n expectations are recursively defined in a way that a player holding level-n expectations correctly predicts the action of an opponent holding level-(n−1) expectations. A general conceptual framework to study such dynamics for two-stage games is developed and it is shown that, contrary to results for single-stage games, the fixed points of the dynamics depend on the level of the expectations. In particular, for level-0 expectation, fixed points correspond to a Nash equilibrium of a simultaneous move version of the game, whereas (under certain conditions) fixed points converge towards the subgame perfect equilibrium of the two-stage game if the level of expectations goes to infinity. The approach is illustrated using a two-stage duopoly game, where firms in the first stage invest in activities reducing their marginal costs and in the second stage engage in Cournot competition. Conditions for local stability of the fixed points are derived for different levels of expectations and it is shown that level-2 expectations are sufficient to move the fixed-point of the dynamics to a close neighborhood of the subgame perfect equilibrium. Furthermore, it is demonstrated that although firms benefit from unilateral increases in the level of expectations, an increase of n by all firms reduces all profits.     

Hotelling was Right

This paper proves existence of a subgame perfect equilibrium in Hotelling's original (unidimensional city, linear transportation costs, uniform distribution of the consumers, two firms with identical and constant marginal cost, perfectly inelastic demand) location–price game such that in the location subgame the location choices of the firms are pure and identical. The result can be extended to variations of the original setup (multidimensional city, nonlinear transportation costs, nonuniform distribution of consumers, many firms with identical and constant marginal costs, two or more firms with nonidentical but constant marginal costs).     

The optimal entry fee-prize ratio in Tullock contests

We analyze a three-stage game where an organizer sets an entry fee for a Tullock contest event, and a finite population of homogeneous agents simultaneously decide whether to participate or not. We show that in the unique symmetric subgame perfect Nash equilibrium, the larger the population size, the lower the probability the agents enter the contest, but the organizer’s optimal entry fee-prize ratio could either increase or decrease with the population size. When the population size approaches infinity, the number of contestants converges to a Poisson distributed random variable.     

Efficient equilibria in a differential game of capitalism

One considers a differential game of capitalism ‘à la Lancaster’. Feedback Nash equilibria and Pareto optimal solutions are characterized under the assumption that the planning horizon is infinite. It is then shown that, by combining a Pareto optimal solution with the Nash feedback equilibrium strategy pair, which plays the role of a threat, one can obtain an efficient equilibrium which is also subgame perfect in the sense of Selten. This result modifies sensibly the previous interpretation of the inherent inefficiency of capitalism.     

Repeated interaction in standard setting

Standardization may allow the owners of standard‐essential patents to charge higher royalties than would have been negotiated ex ante. In practice, however, standard‐setting efforts are often characterized by repeated interaction and complementarities among technologies. These features give firms that contribute technology to standards both the ability and the incentive to avoid excessive royalties by threatening to exclude other technology contributors from future rounds of standardization if they charge royalties exceeding ‘fair, reasonable, and nondiscriminatory’ (FRAND) levels. We show that such an outcome can be sustained as a subgame‐perfect equilibrium of a repeated standard‐setting game and examine how the decision‐making rules of standard‐setting organizations (SSOs) affect the sustainability of FRAND royalties. Our analysis provides a novel justification for super‐majority requirements and other rules frequently adopted by SSOs.     

Ramsey policies in a small open economy with sticky prices and capital

This paper analyzes jointly optimal fiscal and monetary policies in a small open economy with capital and sticky prices. We allow for trade in consumption goods under perfect international risk-sharing. We consider balanced-budget fiscal policies where authorities use distortionary taxes on labor and capital together with monetary policy using the nominal interest rate. First, as long as a symmetric equilibrium is considered, the steady state in an open economy is isomorphic to that of a closed economy. Second, sticky prices’ allocations are almost indistinguishable from flexible prices allocations both in open and closed economies. Third, the open economy dimension delivers results that are qualitatively similar to those of a closed economy but with significant quantitative changes. Tax rates are both more volatile and more persistent to undo the distortions implied by terms of trade fluctuations.     

Dynamic R&D with spillovers: A comment

Cellini and Lambertini [2009. Dynamic R&D with spillovers: competition vs cooperation. J. Econ. Dyn. Control 33, 568–582] study a dynamic R&D game with spillovers. This comment demonstrates that, contrary to what is claimed in their paper, the game is not state redundant and the open-loop Nash equilibrium is not subgame perfect.     

Endogenous vertical structure and trade policy in an import-competing market

We examine the endogenous determination of a vertical market in an import-competing market with import tariff. We show that if firms commit to vertical organization before the government's commitment to trade policy, the home and foreign firms choose vertical separation and vertical integration, respectively, at equilibrium under Bertrand competition. Under Cournot competition, the subgame perfect Nash equilibrium entails both firms separating their retailers. Comparing profits between Bertrand competition to Cournot competition, we find that upstream manufacturer's profit can be higher under Bertrand competition with integration than under Cournot competition with separation when comparing foreign upstream manufacturer's profit.     

Every member of the core is as respectful as any other

We strategically separate different core outcomes. The natural counterparts of a core allocation in a strategic environment are the α-core, the β-core and the strong equilibrium, modified by assuming that utility is transferable in a strategic context as well. Given a core allocation ω of a convex transferable utility (TU) game \(v\), we associate a strategic coalition formation game with \( \left( {v, \omega } \right) \) in which ω survives, while most other core allocations are eliminated. If the TU game is strictly convex, the core allocations respected by the TU-α-core, the TU-β-core and the TU-strong equilibrium shrink to ω only in the canonical family of coalition formation games associated with \( \left( {v, \omega } \right) \). A mechanism, which strategically separates core outcomes from noncore outcomes for each convex TU game according to the TU-strong equilibrium notion is reported.     

A non-cooperative approach to the ordinal Shapley–Shubik rule

In bargaining problems, a rule satisfies ordinal invariance if it does not depend on order-preserving transformations of the agents’ utilities. In this paper, a non-cooperative game for three agents, based on bilateral offers, is presented. The ordinal Shapley–Shubik rule arises in subgame perfect equilibrium as the agents have more time to reach an agreement.     

Matching, search and intermediation with two-sided heterogeneity

This paper analyzes the role played by intermediation in a decentralized market, where trade is carried out through bilateral bargaining, and where the bargaining outcome depends on the process of search for suitable trading partners. To this purpose, a monopolistic intermediary is embedded in a dynamic model of random-matching and two-sided search with heterogeneous agents. It is shown that intermediation might speed up the matching process and might induce separation of the agents’ types, thus enhancing sorting efficiency with respect to a pure search market, where sorting externalities cause multiplicity of equilibria to arise and determine inefficient matching outcomes. Nonetheless, intermediation might also introduce frictions that do not exist in a decentralized market operating in isolation, and this impairs efficiency.      

供应链中双方供应的竞争和合作博弈研究

针对当前供应链中供应方面存在的相关局限性。构造了双方供应和制造商之间的博弈模型。该模型主要特点是双方 供应之间的二阶段博弈所形成的质量和价格策略。在此条件下制造商和供应商之间进行讨价还价。以分配整体利润。指出了供 需双方在讨价还价时存在惟一的子博彝精炼纳什均衡。