Strategic behavior in financial markets

We describe a financial market as a noncooperative game in strategic form. Agents may borrow or deposit money at a central bank and use the cash available to them in order to purchase a commodity for immediate consumption. They derive positive utility from consumption and from having cash reserves at the end of the day, whereas being bankrupt entails negative utility. The bank fixes interest rates. The existence of Nash equilibria (both mixed and pure) of the ensuing game is proved under various assumptions. In particular, no agent is bankrupt at equilibrium. Asymptotic behavior of replica markets is discussed, and it is shown that given appropriate assumptions, the difference between a strategic player and a price taker is negligible in a large economy.     

On pure-strategy Nash equilibria in price–quantity games

This paper examines the existence and characteristics of pure-strategy Nash equilibria in oligopoly models in which firms simultaneously set prices and quantities. Existence of a pure-strategy equilibrium is proved for a class of price–quantity games. If the demand function is continuous, then the equilibrium outcome is similar to that of a price-only model. With discontinuous demand and limited spillover, there are rationing equilibria in which combined production falls short of market demand. Moreover, there might again be an equilibrium reflecting the outcome of a price game. Competition in price and quantity thus yields Bertrand outcomes under a variety of market conditions.     

Convergence in games with continua of equilibria

In game theory, the question of convergence of dynamical systems to the set of Nash equilibria has often been tackled. When the game admits a continuum of Nash equilibria, however, a natural and challenging question is whether convergence to the set of Nash equilibria implies convergence to a Nash equilibrium. In this paper we introduce a technique developed in Bhat and Bernstein (2003) as a useful way to answer this question. We illustrate it with the best-response dynamics in the local public good game played on a network, where continua of Nash equilibria often appear.     

Determinacy of equilibrium in outcome game forms

We show the generic finiteness of the number of probability distributions on outcomes induced by Nash equilibria for two-person game forms such that either (i) one of the players has no more than two strategies or (ii) both of the players have three strategies, and (iii) for outcome game forms with three players, each with at most two strategies. Finally, we exhibit an example of a game form with three outcomes and three players for which the Nash equilibria of the associated game induce a continuum of payoffs for an open non-empty set of utility profiles.     

Price stickiness and markup variations in market games

In this paper, we show that the Shapley–Shubik market game model with production naturally generates an equilibration mechanism that can accommodate price stickiness arising from strategic interactions of firms. Unlike New Keynesian models that show similar price stickiness results, the market game model does not require enforcing menu costs or other additional restraints on price adjustment mechanisms in order to generate price stickiness. As such, we suggest that the market game model can provide a good micro-foundation for macroeconomic analysis. We then explicitly show the relationship between a typical firm’s markup of price over marginal cost and its market share.     

Oligopoly, Financial Structure, and Resolution of Uncertainty

We characterize equilibria of a multistage game in which competing duopolists may acquire and share information in advance of choosing their financial structure which, in turn, precedes production. Given sufficient uncertainty, equilibria exist in which the efficiency and, possibly, coordination gains to acquiring and sharing perfect information are sufficient to break Brander and Lewis's (1986) result wherein both firms issue debt to their mutual disadvantage. However, more interesting may be the robustness of that result when uncertainty is low or when information is imperfect. The key insight is that the consequences of issuing debt are invariant to the level of uncertainty, given that firms can recalibrate the terms of debt to achieve the Stackelberg solution.     

An existence theorem for Cournot–Walras equilibria in a monopolistically competitive economy

We establish an existence theorem for Cournot–Walras equilibria in a monopolistically competitive economy. Instead of the traditional approach which depends on Kakutani’s fixed point theorem, we employ the theories of aggregative games and best reply potential games. We show that, if there exists a representative consumer, under some conditions on preferences and production technologies, the profit maximization game is a (pseudo) best reply potential game. Hence, the existence of the equilibria is proved independently of the well known convex-valued assumption on the best responses. Although our assumptions result in the additive separability on a utility function of a representative consumer, the existence of increasing returns and indivisible productions can be allowed. In our model, it is shown that the game played by firms exhibits strategic substitutes whether the products of firms are substitutes or complements, and this plays an important role for the existence of the equilibria.     

Strategic behavior in non-atomic games

In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player’s belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. We also show that all regular equilibria of smooth non-atomic games are strategic. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games.     

Price Competition When Consumersare Uncertain About Which Firm Sells Which Quality

In this paper we analyze the properties of price equilibria in a duopoly market where firms sell vertically differentiated products, consumers being uncertain about which firm sells which quality. Both existence and properties of price equilibria are characterized by the beliefs of the consumers' population about the distribution of quality between firms.     

Essential stability in games with endogenous sharing rules

We prove that essential games with endogenous sharing rules form a dense residual set and that every game with endogenous sharing rules has at least one minimal essential set of solutions. Furthermore, we establish that essential continuous games form a dense residual set and that every continuous game has at least one minimal essential set of Nash equilibria.     

Markov Perfect equilibria in repeated asynchronous choice games

This paper examines the issue of multiplicity of Markov Perfect equilibria in alternating move repeated games. Such games are canonical models of environments with repeated, asynchronous choices due to inertia or replacement. Our main result is that the number of Markov Perfect equilibria is generically finite with respect to stage game payoffs. This holds despite the fact that the stochastic game representation of the alternating move repeated game is “non-generic” in the larger space of state dependent payoffs. We further obtain that the set of completely mixed Markov Perfect equilibria is generically empty with respect to stage game payoffs.     

The revelation of information in strategic market games: A critique of rational expectations equilibrium

We criticize the R.E.E. approach to asymmetric information general equilibrium because it does not explain how information gets ‘into’ the prices. This leads to well-known paradoxes. We suggest a multiperiod game instead, where the flow of information into and out of prices is explicitly modeled. In our game Nash equilibria (N.E.) (1) generalize Walrasian equilibria to asymmetric information, (2) exist generically, (3) eliminate pure speculation, (4) allow prices to reveal information and markets to become more efficient over time, (5) are consistent with the weak efficient markets hypothesis that tracking past prices is not profitable, (6) yet always lead to higher utility for better informed agents (such as experts). Throughout the paper we use one concrete game. In the last section we prove that there is a broad range of games that would have the same properties.     

Note on the optimality of unemployment equilibria

An equilibrium concept for an economy with rigid prices has been given by Drèze (1975). He formulated a model where for some commodity, either the supplies or the demands are rationed. In this note we discuss ‘unemployment equilibria’, i.e., fixed price equilibria for which the quantity rationing affects the supplies only. It can be proved that there exists a set of unemployment equilibria. Therefore we consider the question whether it is possible to characterize the set of undominated unemployment equilibria.     

Price Competition and Advertising Signals: Signaling by Competing Senders

Can price and advertising be used by vertically differentiated duopolists to signal qualities to consumers? We show that pure price separation is impossible if the vertical differentiation is small, while adding dissipative advertising ensures the existence of separating equilibria. Two simple, but nonstandard, equilibrium refinements are introduced to deal with the multisender nature of the game, and they are shown to produce a unique separating and a unique pooling profile. Pooling results in a zero‐profit Bertrand outcome. Separation gives strictly positive duopoly profits, and dissipative advertising is used by the high‐quality firm when products are sufficiently close substitutes. Finally, compared to the complete‐information benchmark, the separating prices of both firms are distorted upwards when the degree of vertical differentiation is large, and downwards when it is small.     

Selling shares to retail investors: auction vs. fixed price

We analyze the problem of selling shares of a divisible good to a large number of buyers when demand is uncertain. We characterize equilibria of two popular mechanisms, a fixed price mechanism and a uniform price auction, and compare the revenues. While in the auction truthful bidding is a dominant strategy, we find that bidders have an incentive to overstate their demand in the fixed price mechanism. For some parameter values we find that the fixed price mechanism outperforms the auction.     

Convergence to competitive equilibria and elimination of no-trade (in a strategic market game with limit prices)

The strategic market games literature contains many results that predict Walrasian equilibria in the competitive limit. However, they usually come at the expense of ad hoc assumptions that rule out “pathological” no trade equilibria. This paper studies a strategic market game with limit prices. The set of Nash equilibrium allocations of this game converges to the set containing all competitive equilibria and no-trade, when players are replicated. Moreover, two rounds of iterated deletion of weakly dominated strategies eliminate the no-trade equilibria. Hence, replication paired with two rounds of iterated dominance gives a clean prediction of competitive equilibrium.     

Aggregate play and welfare in strategic interactions on networks

In recent work by Bramoullé and Kranton (2007), a model for the provision of public goods on a network was presented and relations between equilibria of such a game and properties of the network were established. This model was further extended to include games with imperfect substitutability in Bramoullé et al. (2014). The vast multiplicity of equilibria in such games along with the dramatic changes in equilibria with small changes in network structure, makes it challenging for a system planner to estimate the maximum social welfare of such a game or to devise interventions that enhance this welfare. Our main results address this challenge by providing for arbitrary networks, close approximations to the maximum social welfare and the maximum aggregate play in terms of only network characteristics such as the maximum degree and independence number. For the special case when the underlying network is a tree, we derive formulas which use only the number of nodes and their degrees. These results allow a system planner to assess aggregate outcomes and design interventions for the game, directly from the underlying graph structure, without enumerating all equilibria of the game, thereby significantly simplifying the planner’s problem. A part of our results can be viewed as a logical extension of Pandit and Kulkarni (2018) where the maximum weighted aggregate effort of the model in Bramoullé and Kranton (2007) was characterized as the weighted independence number of the graph.     

集装箱班轮公司非价格行为分析

国际金融危机以来,班轮运输市场一直处于不景气状态。2011年各大班轮公司采取了打价格战的价格行为,结果损失惨重。2011年底马士基推出了＂天天马士基＂,希望通过非价格竞争扩大服务差异,提高行业壁垒,抢占市场份额。文中利用产业经济学SPC理论中的市场行为理论以及博弈论对这一非价格行为进行了分析。     

Existence of equilibrium in a differential game of spatial competition with advertising

We investigate a differential duopoly game with horizontal product differentiation and advertising efforts aimed at increasing market demand, to show that the standard approach to spatial competition fails to produce a pure-strategy price equilibrium in a dynamic game framework. This holds independently of the shape of the transportation cost function. Then, we introduce an endogenous cost associated with the choice of location and characterise the feedback equilibrium, identifying the necessary and sufficient condition for the existence of the pure-strategy (stationary) price equilibrium. The same condition is singled out for the static game where consumer population is constant. Finally, we show that the static game cannot be viewed as a special case of the dynamic one.