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Clock Games: Theory and Experiments
"... Timing is crucial in situations ranging from currency attacks, to product introductions, to starting a revolution. These settings share the feature that payoffs depend critically on the timing of a few other key players—and their moves are uncertain. To capture this, we introduce the notion of clock ..."
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Cited by 20 (3 self)
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Timing is crucial in situations ranging from currency attacks, to product introductions, to starting a revolution. These settings share the feature that payoffs depend critically on the timing of a few other key players—and their moves are uncertain. To capture this, we introduce the notion of clock games and experimentally test them. Each player’s clock starts on receiving a signal about a payoff relevant state variable. Since the timing of the signals is random, clocks are desynchronized. A player must decide how long, if at all, to delay his move after receiving the signal. We show that (i) equilibrium is always characterized by strategic delay—regardless of whether moves are observable or not; (ii) delay decreases as clocks become more synchronized and increases as information becomes more concentrated; (iii) When moves are observable, players “herd ” immediately after any player makes a move. We then show, in a series of experiments, that key predictions of the model are consistent with observed behavior.
Investment Dynamics with Common and Private Values
, 2006
"... We characterize equilibrium in a dynamic investment game with twodimensional signals, where each firm observes its idiosyncratic cost of investment and a signal correlated with common investment returns. We demonstrate that the onestep property holds and that investmentcost cutoffs fortype1firms ..."
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Cited by 14 (3 self)
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We characterize equilibrium in a dynamic investment game with twodimensional signals, where each firm observes its idiosyncratic cost of investment and a signal correlated with common investment returns. We demonstrate that the onestep property holds and that investmentcost cutoffs fortype1firms (with the high commonvalue signal) and type0 firms (with the low commonvalue signal) satisfy a simple equation that does not depend on the cost distribution. However, “reversals ” are possible, where a large number of firms investing in a given round becomes bad news about investment returns. The optimal investment subsidy can be either positive or negative.
Preemption Games with Private Information. Forthcoming, Review of Economic Studies
, 2011
"... Preemption games are widely used to model economic problems such as patent races. We introduce private information into these games and allow for this information to stochastically change over time. This reflects, e.g. how R&D competitors improve their innovations over time and keep these innov ..."
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Cited by 7 (0 self)
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Preemption games are widely used to model economic problems such as patent races. We introduce private information into these games and allow for this information to stochastically change over time. This reflects, e.g. how R&D competitors improve their innovations over time and keep these innovations secret before patenting them. The analysis initially appears intractable because of the complexity of the equilibrium updating of beliefs on opponents ’ information. However, we demonstrate the existence of a class of equilibria and calculate these equilibria in closed form. We find that the expected durations in these equilibria are longer than when players ’ information is public but, in some cases, shorter than in the collusive outcome. Hence, R&D secrecy slows down innovation disclosure.
Preemption Games: Theory and Experiment ∗
, 2008
"... Several investors face an irreversible investment opportunity whose value V is governed by Brownian motion with upward drift and random expiration. The first investor i to seize the opportunity before expiration receives the current V less a privately known cost Ci; the other investors receive nothi ..."
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Cited by 1 (0 self)
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Several investors face an irreversible investment opportunity whose value V is governed by Brownian motion with upward drift and random expiration. The first investor i to seize the opportunity before expiration receives the current V less a privately known cost Ci; the other investors receive nothing. We characterize Bayesian Nash Equilibrium (BNE) for this game, extending previously known results. We also report a laboratory experiment with 72 subjects randomly matched into 600 triopolies. As predicted in BNE, subjects in triopolies invested at lower values than in monopolies, changes in Brownian parameters significantly altered investment values in monopoly but not in triopoly; and the lowest cost investor in a triopoly usually preempted the others. Evidence was mixed on other BNE predictions, e.g., whether higher cost brings smaller markups. Overall, subjects ’ earnings came rather close to the BNE prediction.
Timing Models with Both Explosive and Timed Entry: Endogenous Herding and The Rush Hour
, 2004
"... There is a vast collection of scenarios where people have to time a decision optimally visavis the decision of other, examples include market entry and exit, corporate restructuring, mergers and acquisitions and so on. In economics these strategic decisions are typically studied with timing games, ..."
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There is a vast collection of scenarios where people have to time a decision optimally visavis the decision of other, examples include market entry and exit, corporate restructuring, mergers and acquisitions and so on. In economics these strategic decisions are typically studied with timing games, either tailoring the question to fit a War of Attrition(having more predecessors helps), or to a preemption game (more predecessors hurts). In this paper we study situations where being neither first nor last or where being either first or last (but not in the middle) is optimal. Our results suggest that our model can explain behavior in a variety of applied settings: as equilibrium outcomes our model variously yields: • an initial War of Attrition ending in a preemptive explosion (fashion) • inaction, a War of Attrition, a preemptive flash (‘palm pilot ’ market) • a preemptive entry explosion, and a War of Attrition (the Gold Rush) • inaction, a slow preemption game, and a War of Attrition (rush hour) The time and size of herdlike atomic entry is always endogenous, and in each case, anticipation of later timing games influences current play — from swelling the magnitude of preemptive explosions to truncating wars of attrition.
© 2004 INFORMS Strategically Seeking Service: How Competition Can Generate Poisson Arrivals
"... We consider a simple game in which strategic agents select arrival times to a service facility. Agents find congestion costly and, hence, try to arrive when the system is underutilized. Working in discrete time, we characterize purestrategy Nash equilibria for the case of ample service capacity. In ..."
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We consider a simple game in which strategic agents select arrival times to a service facility. Agents find congestion costly and, hence, try to arrive when the system is underutilized. Working in discrete time, we characterize purestrategy Nash equilibria for the case of ample service capacity. In this case, agents try to spread themselves out as much as possible and their selfinterested actions will lead to a socially optimal outcome if all agents have the same wellbehaved delay cost function. For even modest sized problems, the set of possible purestrategy Nash equilibria is quite large, making implementation potentially cumbersome. We consequently examine mixedstrategy Nash equilibria and show that there is a unique symmetric Nash equilibrium. Not only is this equilibrium independent of the number of agents and their individual delay cost functions, the arrival pattern it generates approaches a discretetime Poisson process as the number of agents and arrival points gets large. Our results extend to the case of time varying preferences. With an appropriate initialization, the results also extend to a system with limited capacity. Our model lends support to the traditional literature on managing service systems. This work has generally ignored customers strategically choosing arrival times. Rather it is commonly assumed that customers seek service according to some wellbehaved process (e.g., that interarrival times follow a renewal process). We show that assuming Poisson arrivals is an acceptable assumption even with strategic customers if the population is large and the horizon is long.
NPlayer Preemption Games
, 2005
"... This paper studies in
nite horizon complete information preemption games with N players. We consider a continuous time model where
rms have to choose a point in time at which they seize an opportunity to make an irreversible onetime investment. Upon investment,
rms compete with other
rms that h ..."
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This paper studies in
nite horizon complete information preemption games with N players. We consider a continuous time model where
rms have to choose a point in time at which they seize an opportunity to make an irreversible onetime investment. Upon investment,
rms compete with other
rms that have already invested. Flow pro ts are declining in the number of investors but the cost of investing declines over time. Our model captures environments such as new product introduction or entry into a growing market. We show that there exists a unique subgame perfect Nash equilibrium outcome. Payo¤s are equalized. Firms investments can be clustered, although coordination failures are ruled out and investment is rivalrous. Increasing the number of competitors in the investment game does not necessarily accelerate investment. In particular, the
rst investment in the twoplayer game is a lower bound for the
rst investment in any Nplayer game with linear Cournot competition.
Interdependent Durations ∗
, 2007
"... This paper studies the identification and estimation of a simultaneous equation model where the variable of interest is a duration measure. It proposes a game theoretic model in which durations are determined by strategic agents. In the absence of strategic motives, the model delivers a version of t ..."
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This paper studies the identification and estimation of a simultaneous equation model where the variable of interest is a duration measure. It proposes a game theoretic model in which durations are determined by strategic agents. In the absence of strategic motives, the model delivers a version of the generalized accelerated failure time model. In its most general form, the system resembles a classical simultaneous equation model in which endogenous variables interact with observable and unobservable exogenous components to characterize a certain economic environment. In this paper, the endogenous variables are the individually chosen equilibrium durations. Even though a unique solution to the game is not always attainable in this context, the structural elements of the economic system are shown to be semiparametrically point identified. We also present a brief discussion of estimation ideas and a set of simulation studies on the model. JEL Codes: C10, C30, C41. ∗Versions of this paper at different stages were presented to various audiences. We thank these audiences for their many comments. In particular we thank Herman Bierens, Wilbert van der Klaauw, Rob Porter, Elie Tamer, Giorgio Topa and Quang Vuong for their insights. Any remaining mistakes are ours only.