Symmetric equilibrium strategies in game theoretic real option models

This paper considers the problem of investment timing under uncertainty in a duopoly framework. When both firms want to be the first investor a coordination problem arises. Here, a method is proposed to deal with this coordination problem, involving the use of symmetric mixed strategies.     

Rationalizability in continuous games

Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating “never-best-reply” strategies terminates before or at the first uncountable ordinal, and this bound is tight. Also, we examine the connection between this process and common belief of rationality in the universal type space of Mertens and Zamir (1985).     

Micro-interaction dynamics in group decision making: Face games, interaction order and boundary work

Drawing on Goffman's face theory, this paper documents and interprets the micro interaction dynamics underlying group decision making within a consultancy task force. Our analysis suggests that decision making is an instance of strategic face-to-face behavior where individuals seek to influence each other and reach decisions by means of face-work and self-presentation tactics. Moreover, face-to-face behavior generates an ‘interaction order’ that frames the decision making situation and constrains further interactions among decision makers. We discuss the implications that can be drawn from the observed case by relating our findings to the emergent stream of studies on micro-decision making.     

电子商务之网游

截止2006年,中国网民的数量已经达到13700万人。虽然网民总数多,增长快,但是互联网普及程度还很低。未来的发展空氓粱很大。而网游的力量是不可忽视的,所以将电子商务和网游结合起来是企业拓展盈利的一个新的方向。文中从中国网民现状。中国网游现状,中国电子商务现状及电子商务与网游的结合进行了讨论。     

A note on the evaluation of information in zero-sum repeated games

Two players play a zero-sum repeated game with incomplete information. Before the game starts one player receives a private signal that depends on the realized state of nature. The rules that govern the choice of the signal are determined by the information structure of the game. Different information structures induce different values. The value-of-information function of a game associates every information structure with the value it induces. We characterize those functions that are value-of-information functions for some zero-sum repeated game with incomplete information.     

Strategic real options under asymmetric information

This paper studies the effect of private information on the capital allocation decisions of firms who operate under imperfect competition. I analyze two interactive firms, one with private information and the other without, who must decide when to undertake an irreversible and uncertain investment decision. Traditional non-strategic models of irreversible investment under uncertainty involve a single decision maker and result in an optimal period of delay before the investment is undertaken. In a strategic setting, firms must balance their desire to delay against competitive advantages from early investment. I find that an equilibrium may not exist within the standard continuous framework when the private information is over revenues. Moreover, when an equilibrium does exist the competitive pressures from the uninformed firm are weak. This is in contrast to existing models with asymmetric information over costs, where an equilibrium always exists and the competitive pressures remain strong (Hsu and Lambrecht, 2007). This work shows that the investment timing decision, and thus the value of the private information, is highly sensitive to the nature of incomplete information.     

会计师事务所的进入、退出与审计市场的竞争

本文主要从进入、退出的角度研究审计市场的竞争。本文的分析表明,审计市场的市场占有率变动率更为合理地衡量市场的动态变化,审计市场的进入壁垒主要是准入壁垒(管制壁垒),而结构性壁垒和流动性壁垒主要存在于大客户市场,对于小客户市场的影响作用很小。为了防止进入者的进入,在位者通过各种流动性壁垒的设置以提高进入者的成本。但从总体看,审计市场仍然是高度竞争的。     

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.     

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     

Elections and strategic positioning games

We formalize the interplay between expected voting behavior and strategic positioning behavior of candidates as a common agency problem in which the candidates (i.e., the principals) compete for voters (i.e., agents) via the issues they choose and the positions they take. A political situation is defined as a feasible combination of candidate positions and expected political payoffs to the candidates. Taking this approach, we are led naturally to a particular formalization of the candidates' positioning game, called a political situation game. Within the context of this game, we define the notion of farsighted stability (introduced in an abstract setting by Chwe 1994) and apply Chwe's result to obtain existence of farsightedly stable outcomes. We compute the farsightedly stable sets for several examples of political situations games, with outcomes that conform to real-world observations.Received: 18 May 2001, Accepted: 22 January 2002, JEL Classification: C7, D7, D8Myrna H. Wooders: http://www.warwick.ac.uk/fac/soc/Economics/wooders/An earlier version of this paper was completed while the first author was visiting the Department of Economics, University of Exeter. The first author gratefully acknowledges Exeter's support and hospitality. Similarly, the second author gratefully acknowledges the support and hospitality of the Centre for Operations Research and Econometrics (CORE) of the University of Louvain-la-Neuve, Belgium and of the University of Cergy-Pontoise, France. Both authors are indebted to Amrita Dhillon, John Duggan and Gilat Levy for helpful comments about references. Both authors thank an anonymous referee for helpful comments.     

Recurrent crises in global games

Global games have unique equilibria in which aggregate behavior changes sharply when an underlying random fundamental crosses some threshold. This property relies on the existence of dominance regions: all players have a highest and lowest action that, for some fundamentals, is strictly dominant. But if the fundamental follows a random walk, it eventually spends nearly all of its time in these regions: crises gradually disappear. We obtain recurring crises by adding a single large player who lacks dominance regions. We also show that in order to obtain recurring crises, one must either relax dominance regions or restrict to fundamentals that continually return to or cross over a fixed region.     

Generic finiteness of equilibrium payoffs for bimatrix games

It is shown that in any affine space of payoff matrices the equilibrium payoffs of bimatrix games are generically finite.     

Evolving densities in continuous strategy games through particle simulations

Many cases of strategic interaction between agents involve a continuous set of choices. It is natural to model these problems as continuous space games. Consequently, the population of agents playing the game will be represented with a density function defined over the continuous set of strategy choices. Simulating evolutionary dynamics on continuous strategy spaces is a challenging problem. The classic approach of discretizing the strategy space is ineffective for multidimensional strategy spaces. We present a principled approach to simulation of adaptive dynamics in continuous space games using sequential Monte Carlo methods. Sequential Monte Carlo methods use a set of weighted random samples, also named particles to represent density functions over multidimensional spaces. Sequential Monte Carlo methods provide computationally efficient ways of computing the evolution of probability density functions. We employ resampling and smoothing steps to prevent particle degeneration problem associated with particle estimates. The resulting algorithm can be interpreted as an agent based simulation with elements of natural selection, regression to mean and mutation. We illustrate the performance of the proposed simulation technique using two examples: continuous version of the repeated prisoner dilemma game and evolution of bidding functions in first-price closed-bid auctions.     

Non-cooperative games on hyperfinite Loeb spaces

We present a particular class of measure spaces, hyperfinite Loeb spaces, as a model of situations where individual players are strategically negligible, as in large non-anonymous games, or where information is diffused, as in games with imperfect information. We present results on the existence of Nash equilibria in both kinds of games. Our results cover the case when the action sets are taken to be the unit interval, results now known to be false when they are based on more familiar measure spaces such as the Lebesgue unit interval. We also emphasize three criteria for the modelling of such game-theoretic situations—asymptotic implementability, homogeneity and measurability—and argue for games on hyperfinite Loeb spaces on the basis of these criteria. In particular, we show through explicit examples that a sequence of finite games with an increasing number of players or sample points cannot always be represented by a limit game on a Lebesgue space, and even when it can be so represented, the limit of an existing approximate equilibrium may disappear in the limit game. Thus, games on hyperfinite Loeb spaces constitute the ‘right' model even if one is primarily interested in capturing the asymptotic nature of large but finite game-theoretic phenomena.     

Entry and barriers to entry in emerging markets

This note briefly introduces the symposium on entry and entry barriers in emerging markets edited by Nauro Campos and Saul Estrin. The symposium contains four inter-related case studies focusing in depth on the relationship between entry of new firms and institutional arrangements in four major emerging markets: Brazil, China, India and Russia. We find that entry rates are not necessarily low in emerging markets, and that institutional quality is a complex and “fuzzy” notion so that its impact on the entry process is not straightforward.     

Endogenous mechanisms and Nash equilibrium in competitive contracting games

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm’s catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism—and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.     

Learning about learning in games through experimental control of strategic interdependence

We report results from an experiment in which humans repeatedly play one of two games against a computer program that follows either a reinforcement or an experience weighted attraction learning algorithm. Our experiment shows these learning algorithms detect exploitable opportunities more sensitively than humans. Also, learning algorithms respond to detected payoff-increasing opportunities systematically; however, the responses are too weak to improve the algorithms' payoffs. Human play against various decision maker types does not vary significantly. These factors lead to a strong linear relationship between the humans' and algorithms' action choice proportions that is suggestive of the algorithms' best response correspondences.     

Negotiation games with unobservable mixed disagreement actions

A negotiation model combines an alternating offers bargaining game with a normal form stage game that determines players’ (interim) disagreement payoffs. Busch and Wen [Econometrica 63 (1995) 545] investigated this negotiation model under the assumption that players’ past mixed disagreement actions are observable. The question arises if this assumption is a substantial restriction. In this paper, we adopt the more plausible assumption that only the realizations of past mixed actions are observable, and find that the set of equilibrium payoffs shrinks, compared to that when mixed disagreement actions are observable. We precisely identify the effects of the unobservability and characterize the limiting set of equilibrium payoffs as the two players become sufficiently patient.