Subjective Expected Utility Theory with State-Dependent Preferences

This paper extends Savage′s subjective expected utility theory to include state-dependent preferences. The dependence of the decision maker′s preferences over consequences on the states of nature is represented by state-specific mappings of the set of consequences onto itself. Within this framework Savage′s postulates are reformulated and it is shown that there exist subjective expected utility representations of the preference relation over acts with unique, nonatomic, probability measure on the algebra of all events, and a state-dependent utility function over the set of consequences. Journal of Economic Literature Classification Number: D81.     

Overlapping expectations and Hart's conditions for equilibrium in a securities model

Hart (J. Econ. Theory9 (1974), 293–311) gave conditions for equilibrium to exist in a securities model where each agent undertakes asset transactions to maximize expected utility of wealth. These conditions rule out agents wanting to undertake unbounded balanced transactions to reach a Pareto superior allocation given their expectations. With mild extra assumptions to make agents unwilling to risk incurring unbounded losses on their portfolios, Hart's conditions become equivalent to an assumption of “overlapping expectations,” which is comparable to a much weaker form of Green's “common expectations” (Econometrica41 (1973), 1103–1124).     

A cake for Cournot

A cake division mechanism is presented that is equivalent in terms of the size of the pieces of the cake n players’ receive in equilibrium to the quantities that n firms in a Cournot oligopoly supply in equilibrium. This mechanism extends to equivalence between cake division and Nash’s ‘divide the dollar’ game.     

What Is Distinctive about China′s Economic Transition? State Enterprise Reform and Overall System Transformation

Entry of nonstate industrial firms has played a crucial role in China′s reform process by creating markets and competition. Yet the state-owned sector has also performed adequately, improving incentives and productivity, and turning in a respectable growth performance. Moderate improvements in the state sector have thus supported a virtuous cycle of reform. Simple contrasts between state and private ownership systems therefore explain little of China′s apparently successful combination of reform and growth. J. Comp. Econom., June 1994, 18(3), 470-490. University of California, San Diego, La Jolla, California 92093-0519.     

Firm Scale and the Endogenous Timing of Entry: a Choice between Commitment and Flexibility

This paper presents a model of stochastic oligopoly with demand uncertainty where firms endogenously choose entry timing. We examine two extreme types of market structure and show that the equilibrium correspondence that connects them is continous. With two identically sized firms, there are symmetric, Cournot type equilibria where the probability of early entry declines with greater uncertainty, and for low uncertainty two asymmetric equilibria. With one large firm with a continuum of nonatomic firms, there is a unique Stackelberg equilibrium. We conclude that the behavior of a dominant firm with a finite fringe can be approximated by Stackelberg equilibrium.Journal of Economic LiteratureClassification Numbers?: D21, L11.     

The Role of Absolute Continuity in “Merging of Opinions” and “Rational Learning”

D. Blackwell and L. Dubins (1962, Ann. Math. Statist.38, 882–886) showed that opinions merge when priors are absolutely continuous. E. Kalai and E. Lehrer (1993, Econometrica61, 1019–1045) use this result to show that players in a repeated game eventually play like a Nash equilibrium. We provide an alternative proof of merging of opinions that clarifies the role of absolute continuity while casting doubt on the relevance of the result. Persistent disagreement, the opposite of merging, allows the construction of a sequence of mutually favorable “bets.” By a law of large numbers, both agents are certain they will win these bets on average. This certain disagreement violates absolute continuity. Journal of Economic Literature Classification Numbers: C11, C69, C72, D83.     

The Art of Reforming Centrally Planned Economies: Comparing China, Poland, and Russia

The three reasons for gradualism, (1) agricultural reform should precede industrial reforms, (2) state-owned enterprises (SOEs) can be reformed, and (3) economic liberalization should precede political liberalization, are not generalizable. China′s gradualism is the product of political deadlock over the final form of the economy. China has been most successful in the areas where reforms have been radical and lackluster where reforms have been incremental. The output performance across reforming countries reflected differences mainly in economic structures rather than in policies. China′s growth comes from the movement of surplus agricultural labor into industry, and Poland′s and Russia′s decline come from the closing of noncompetitive enterprises to release factors of production to the new efficient enterprises. J. Comp. Econom., June 1994, 18(3), pp. 000-000. University of California, Davis, California 95616-8617.     

A Noncooperative Analysis of Hotelling's Location Game

We study the location equilibrium in Hotelling's model of spatial competition. As d'Aspremontet al.have shown, with quadratic consumer transportation cost the two sellers will seek to move as far away from each other as possible. We show that the location game possesses an infinity of mixed strategy Nash equilibria. In these equilibria coordination failure invalidates the principle of “maximum differentiation” and firms may even locate at the same point.Journal of Economic LiteratureClassification Numbers: C72, D43, L11.     

Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives

In a game of a finite number of repetitions of a Cournot-type model of an industry, if firms are satisfied to get close to (but not necessarily achieve) their optimal responses to other firms' sequential strategies, then in the resulting noncooperative “equilibria” of the sequential market game, (1) if the lifetime of the industry is large compared to the number of firms, there are equilibria corresponding to any given duration of the cartel, whereas (2) if the number of firms is large compared to the industry's lifetime, all equilibria will be close (in some sense) to the competitive equilibrium.     

Coordination, “Magic,” and Reinforcement Learning in a Market Entry Game

Previous experimental studies have documented quick convergence to equilibrium play in market entry games with a large number of agents. The present study examines the effect of the available information in a 12-player game in an attempt to account for these findings. In line with the prediction of a simple reinforcement learning model (Roth and Erev, 1995,Games Econ. Behav.8, 164–212), quick convergence to equilibrium is observed even given minimal information (unknown payoff rule). However, in violation of the basic model, information concerning other players' payoff increases the number of entrants. The information effect can be described by a variant of the basic reinforcement learning model assuming that the additional information changes the player's reference point.Journal of Economic LiteratureClassification Number: C7, C92.     

Mixed-Strategy Nash Equilibrium Based upon Expected Utility and Quadratic Utility

The notion of a mixed-strategy Nash equilibrium suffers from three inherent difficulties. First, given the equilibrium strategies of other players, there are many best replies. Second, the equilibrium is unstable. Third, comparative statics results are counterintuitive. We demonstrate that these difficulties all have their origin in von Neumann and Morgenstern′s expected utility. In contrast, players with "quadratic utility" have unique best replies and the Nash equilibrium appears to yield intuitive comparative statics results. Journal of Economic Literature Classification Number: C72.     

Sequential Equilibrium and Competition in a Diamond–Dybvig Banking Model

Within the framework of a Diamond–Dybvig model [J. Polit. Econ.91(1983), 401–419], but with explicitly modelling the autarky choice during the planning period, we demonstrate that a mixed strategy bank run equilibrium that does not rely on sunspots may coexist with the sunspot run equilibrium previously studied in the literature. In a version of the model with multiple banks, there exist sequential equilibria that imply positive profits. However, the zero-profit contract in which runs never occur can be supported as the unique equilibrium outcome if the agents play pure strategies only and their beliefs are restricted to be consistennt with a forward induction argument.Journal of Economic LiteratureClassification Numbers: C72, G21     

Propping and tunneling

In countries with weak legal systems, there is a great deal of tunneling by the entrepreneurs who control publicly traded firms. However, under some conditions entrepreneurs prop up their firms, i.e., they use their private funds to benefit minority shareholders. We provide evidence and a model that explains propping. In particular, we suggest that issuing debt can credibly commit an entrepreneur to propping, even though creditors can never take possession of any underlying collateral. This helps to explain why emerging markets with weak institutions sometimes grow rapidly and why they are also subject to frequent economic and financial crises. Journal of Comparative Economics 31 (4) (2003) 732–750.     

Infinite Histories and Steady Orbits in Repeated Games

We study a model of repeated games with the following features: (a) Infinite histories. The game has been played since days of yore, or is so perceived by the players: (b) Turing machines with memory. Since regular Turing machines coincide with bounded recall strategies (in the presence of infinite histories), we endow them with "external" memory; (c) Nonstrategic players. The players ignore complicated strategic considerations and speculations about them. Instead, each player uses his/her machine to update some statistics regarding the others′ behaviour, and chooses a best response to observed behaviour. Relying on these assumptions, we define a solution concept for the one shot game, called steady orbit. The (closure of the) set of steady orbit payoffs strictly includes the convex hull of the Nash equilibria payoffs and is strictly included in the correlated equilibria payoffs. Assumptions (a)–(c) above are independent to a large extent. In particular, one may define steady orbits without explicitly dealing with histories or machines.     

p-Best response set and the robustness of equilibria to incomplete information

In this paper, we use p-best response sets—a set-valued extension of p-dominance—in order to provide a new sufficient condition for the robustness of equilibria to incomplete information: if there exists a set S which is a p-best response set with , and there exists a unique correlated equilibrium μ^* whose support is in S then μ^* is a robust Nash equilibrium.     

Learning Dynamics in Games with Stochastic Perturbations

Consider a generalization of fictitious play in which agents′ choices are perturbed by incomplete information about what the other side has done, variability in their payoffs, and unexplained trembles. These perturbed best reply dynamics define a nonstationary Markov process on an infinite state space. It is shown, using results from stochastic approximation theory, that for 2 × 2 games it converges almost surely to a point that lies close to a stable Nash equilibrium, whether pure or mixed. This generalizes a result of Fudenherg and Kreps, who demonstrate convergence when the game has a unique mixed equilibrium. Journal of Economic Literature Classification Numbers: 000, 000, 000.     

To Commit or Not to Commit: Endogenous Timing in Experimental Duopoly Markets

In this paper we experimentally investigate the extended game with action commitment of Hamilton and Slutsky (1990, Games Econ. Behavior2, 29–46). In their duopoly game firms can choose their quantities in one of two periods before the market clears. If a firm commits to a quantity in period 1, it does not know whether the other firm also commits early. By waiting until period 2, a firm can observe the other firm's period-1 action. Hamilton and Slutsky predicted the emergence of endogenous Stackelberg leadership. Our data, however, do not confirm the theory. While Stackelberg equilibria are extremely rare, we often observe endogenous Cournot outcomes and sometimes collusive play. This is partly driven by the fact that endogenous Stackelberg followers learn to behave in a reciprocal fashion over time, i.e., they learn to reward cooperation and to punish exploitation. Journal of Economic Literature Classification Numbers: C72, C92, D43.     

Games with Imperfectly Observable Commitment

[1]claims that, in models of commitment, “the first-mover advantage is eliminated when there is aslightamount of noise associated with the observation of the first-mover's selection.” We show that the validity of this claim depends crucially on the restriction to pure strategy equilibria. The game analyzed by Bagwell always has a mixed equilibrium that is close to the Stackelberg equilibrium when the noise is small. Furthermore, an equilibrium selection theory that combines elements from the theory of[7]with elements from the theory of [6], actually selects this “noisy Stackelberg equilibrium.”Journal of Economic LiteratureClassification Number: C72.     

Externalities, expectations, and growth

Summary. The paper studies a model of accumulation and growth where a continuum of heterogeneous firms play dynamically optimal strategies along a (rational expectations) equilibrium. The key feature of the model is that firms' technological decisions are assumed subject to both friction and external effects. This gives rise to a wide multiplicity of equilibrium behavior, any path of sustained growth requiring that the economy tackle a never-ending chain of fresh coordination problems. This setup is modelled as a (non-atomic) dynamic game, suitable conditions being provided that partially characterize when sustained growth is a possible (never the unique) equilibrium outcome. Received: May 25, 1995; revised version: March 25, 1998     

How Successful Has Chinese Enterprise Reform Been? Pitfalls in Opposite Biases and Focus

We analyze two new data sets: one on state-owned enterprises (SOEs) and another on town and village enterprises (IVEs). We find zero TFP growth in SOEs and positive TFP growth in COEs. The evidence suggests that the positive TFP growth in SOEs found by some recent studies might be due to underdeflation of gross output and overdeflation of intermediate inputs. The criterion for successful SOE reform should also include intertemporal efficiency and SOEs′ contribution so macroeconomic stability. Increases in technical efficiency do not necessarily improve SOEs′ financial performance. SOE personnel have received an increasing proportion of value added, hence creating a fiscal crisis for the state. J. Comp. Econom., June 1994, 18(3), pp. 410-437. University of California, Davis, California 95616; Fort Lewis College, Durango, Colorado 81301; University of California, Davis, California 95616; and Chinese Academy of Social Sciences, Beijing 100836, People′s Republic of China.