Tacit Coordination in a Decentralized Market Entry Game with Fixed Capacity

Tacit coordination is studied experimentally in a class of iterated market entry games with a relatively small number of potential entrants (n = 6), symmetric players, and fixed entry fees. These games are intended to simulate a situation where a newly emergent market opportunity may be fruitfully exploited by no more than a fixed and commonly known number of firms. Our results indicate a high degree of sensitivity to the game parameters that are manipulated in the study, namely, the market capacity, entry fee, and method of subject assignment to groups (fixed vs. random), as well as sophisticated adaptation to actual and hypothetical changes in wealth level. We find no support for convergence to equilibrium play on either the aggregate or individual level or for any trend across rounds of play to maximize total group payoff by lowering the frequency of entry. The coordination failure is attributed to certain features of the payoff function that induce strong competition in the attempt to penetrate the market.Tacit Coordination, Market Entry Game, Experiment

Unique bid auctions: Equilibrium solutions and experimental evidence

Two types of auction were introduced on the Internet a few years ago and have rapidly been gaining widespread popularity. In both auctions, players compete for an exogenously determined prize by independently choosing an integer in some finite and common strategy space specified by the auctioneer. In the unique lowest (highest) bid auction, the winner of the prize is the player who submits the lowest (highest) bid, provided that it is unique. We construct the symmetric mixed-strategy equilibrium solutions to the two auctions, and then test them in a sequence of experiments that vary the number of bidders and size of the strategy space. Our results show that the aggregate bids, but only a minority of the individual bidders, are accounted for quite accurately by the equilibrium solutions.

Choice of Prizes Allocated by Multiple Lotteries with Endogenously Determined Probabilities

We study a class of interactive decision making situations in which each agent must choose to participate in one of several lotteries with commonly known prizes. In contrast to the widely studied paradigm of choice between gambles in individual decision making under risk, the probability of winning a prize in each of the lotteries in our study is endogenously determined. In particular, for each lottery, it is known to decrease in the number of agents choosing to play that lottery. We construct the Nash equilibrium solution to this game and then test it experimentally in the special case where each lottery yields only a single prize. The results show a remarkable degree of tacit coordination that supports the equilibrium solution under the assumption of common risk-aversion. However, this coordination is not achieved via individual level randomization. Rather, the entry decisions of most of the subjects can be characterized by local adjustments to the outcome of the previous iteration of the same game along the lines suggested by anticipatory learning models.Coordination, Endogenously Determined Probabilities

Unique bid auctions: Equilibrium solutions and experimental evidence

Two types of auction were introduced on the Internet a few years ago and have rapidly been gaining widespread popularity. In both auctions, players compete for an exogenously determined prize by independently choosing an integer in some finite and common strategy space specified by the auctioneer. In the unique lowest (highest) bid auction, the winner of the prize is the player who submits the lowest (highest) bid, provided that it is unique. We construct the symmetric mixed-strategy equilibrium solutions to the two auctions, and then test them in a sequence of experiments that vary the number of bidders and size of the strategy space. Our results show that the aggregate bids, but only a minority of the individual bidders, are accounted for quite accurately by the equilibrium solutions.unique bid auctions; equilibrium analysis; experiment

Potential Maximization and Coalition Government Formation

A model of coalition government formation is presented in which inefficient, non-minimal winning coalitions may form in Nash equilibrium. Predictions for five games are presented and tested experimentally. The experimental data support potential maximization as a refinement of Nash equilibrium. In particular, the data support the prediction that non-minimal winning coalitions occur when the distance between policy positions of the parties is small relative to the value of forming the government. These conditions hold in games 1, 3, 4 and 5, where subjects played their unique potential-maximizing strategies 91, 52, 82 and 84 percent of the time, respectively. In the remaining game (Game 2) experimental data support the prediction of a minimal winning coalition. Players A and B played their unique potential-maximizing strategies 84 and 86 percent of the time, respectively, and the predicted minimal-winning government formed 92 percent of the time (all strategy choices for player C conform with potential maximization in Game 2). In Games 1, 2, 4 and 5 over 98 percent of the observed Nash equilibrium outcomes were those predicted by potential maximization. Other solution concepts including iterated elimination of dominated strategies and strong/coalition proof Nash equilibrium are also tested.Coalition formation, Potential maximization, Nash equilibrium refinements, Experimental study, Minimal winning

Invariance failure under subgame perfectness in sequential bargaining

A basic property of any normative theory of decision making --- individual or group --- is its invariance under the theory's own equivalence specification. Growing evidence from experimental studies in several areas of game playing indicates that the game-theoretic notion of strategic equivalence is systematically violated in the behavioral arena. The present study expands the design of previous studies of bilateral bargaining by including a third party and a new trading rule - -- modifications which induce behavioral patterns that reject equivalence under subgame perfectionbargaining, subgame perfect, invariance

Time and uncertainty in resource dilemmas : equilibrium solutions and experimental results

Most common pool resource (CPR) dilemmas share two features: they evolve over time and they are managed under environmental uncertainties. We propose a finite-horizon, stochastic, dynamic model that integrates these two dimensions. A distinguishing feature of our model is that the duration of the game is determined endogenously by the players’ collective decisions. In the proposed model, if the resource stock level below which the irreversible event occurs is known in advance, then the optimal resource use coincides with a unique symmetric equilibrium that guarantees survival of the resource. As the uncertainty about the threshold level increases, resource use increases if users adopt decision strategies that quickly deplete the resource stock; however, resource use decreases if they adopt path strategies guaranteeing that the unknown threshold level is never exceeded. Our experimental results show that CPR users frequently implement decision strategies that terminate the game immediately. When the uncertainty about the resource level is reduced, users maintain a positive resource level for a longer duration.Fundação para a Ciência e a Tecnologia (FCT) - SFRH/BSAB/1226/2012, SFRH/BSAB/1159/2011Water Science and Policy Cente

Linking appropriation of common resources and provision of public goods decreases rate of destruction of the commons

Experimental studies of common pool resource (CPR) dilemmas are frequently terminated with collapse of the resource; however, there is considerable evidence in real-world settings that challenge this finding. To reconcile this difference, we propose a two-stage model that links appropriation of the CPR and provision of public goods in an attempt to explain the emergence of cooperation in the management of CPRs under environmental uncertainty. Benchmark predictions are derived from the model, and subsequently tested experimentally under different marginal cost-benefit structures concerning the voluntary contribution to the provision of the good. Our results suggest that the severity of the appropriation problem is significantly mitigated by the presence of an option for voluntarily contributing a fraction of the income surplus from the appropriation phase to the provision of the public good

A Comparison of the Eigenvalue Method and The Geometric Mean Procedure for Ratio Scaling

The development of analytical procedures and experimental techniques for constructing ratio measurement scales has long been a major topic and important challenge in psychophysics and other areas of psychology. The interest in ratio scales is obviously related to their high level of invariance (unique up to a similarity transformation) and the associated statistical operations they allow one to perform (Stevens, 1946). To obtain ratio scales, Stevens and his colleagues " (Stevens, Mack, & Stevens, 1960) developed the "cross modality matching" paradigm, which was originally applied to variables with a corresponding physical continuum and later generalized to social and other psychological stimuli (e.g., Lodge, 'a 1981). Although Stevens' techniques have been widely used in numerous areas (e.g., Stevens, 1972, 1975; Lodge, 1981), their precise characterization is still a topic of debate among measurement specialists (e.g., Shepard, 1981)

Elicitation of strategies in four variants of a round-robin tournament: the case of Goofspiel

Goofspiel is a simple two-person zero-sum game for which there exist no known equilibrium strategies. To gain insight into what constitute winning strategies, we conducted a round-robin tournament in which participants were asked to provide computerized programs for playing the game with or without carryover. Each of these two variants was to be played under two quite different objective functions, namely, maximization of the cumulative number of points won across all opponents (as in Axelrod's tournament), and maximization of the probability of winning any given round. Our results show that there are, indeed, inherent differences in the results with respect to the complexity of the game and its objective function, and that winning strategies exhibit a level of sophistication, depth, and balance that are not captured by present models of adaptive learning