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Abstract:
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

Abstract:
The Braess Paradox (BP) in traffic and communication networks is a powerful illustration of the possible counterintuitive implications of the Nash equilibrium solution. It shows that, paradoxically, when one or more links are added to a weighted network with linear costs that depend on congestion with an attempt to improve it, and each user independently seeks her best possible route, then the equilibrium cost of travel of all users may increase. Extending previous research by Rapoport et al. (2005), we report the results of a new experiment with a richer topology and asymmetric link costs of travel designed to assess the descriptive power of the BP. Our results show that with experience in traversing the network players' choice frequencies approach the equilibrium solution as implied by the BP.

Braess Paradox, traffic networks, linear costs, route choice, experiment

Abstract:
We study search behavior in a generalized "secretary problem" environment in which consumers search sequentially for the best alternative from a known and finite set of multi-attribute alternatives. In contrast to most previous studies, we make no distributional assumptions about the quality of the alternatives. Rather, at each stage of the search the consumers are only assumed to be able to rank order the alternatives they have already inspected in terms of their overall quality. Our study departs from previous experimental investigations of the secretary problem by including search costs and allowing for recall (backward solicitation) of previously inspected alternatives. Both the number of alternatives and the cost of searching are manipulated experimentally in a factorial design. In the no-cost condition, we find that subjects do not search enough, whereas in the cost condition they search too much. We propose a simple behavioral decision model that incorporates both local and global patterns of the sequence - patterns that should have been ignored by a rational consumer - and then show that it can account for the major patterns of the observed results.

Search Behavior, Sequential Choice Models, Information Processing

Abstract:
The Braess paradox (Braess, 1968) consists of showing that, in equilibrium, adding a new link that connects two routes running between a common origin and common destination may raise the travel cost for each network user. We report the results of two experiments designed to study whether the paradox is behaviorally realized in two simulated traffic networks that differ from each other in their topology. Implementing a within-subjects design, both experiments include finite populations of paid participants in a computer-controlled setup who independently and repeatedly choose travel routes in one of two types of traffic networks, one without the added links and the other with the added links, to minimize their travel costs. Our results reject the hypothesis that the paradox is of marginal value and its force, if at all evident, diminishes with experience. Rather, they strongly support the alternative hypothesis that with experience in traversing the traffic network players converge to choosing the Pareto deficient equilibrium routes despite sustaining a sharp decline in their earnings.

Braess Paradox, congested traffic networks, choice of routes, experimental study

Abstract:
We study experimentally a class of pure coordination games as a special case of the Consumer Choice of Prizes game developed by Rapoport et al. (2000). We find a high level of group coordination coupled with considerable switching in the choice of locations. Two models are proposed and tested to account for the results, one postulating the formation of conventions, and the other invoking the mixed strategy equilibrium solution for risk-neutral players. We reject both models as possible candidates to describe the behavioral regularities that we observe in the data. A third model that allows individual perturbations of commonly shared choice probabilities is proposed and tested. It accounts for the major results on the individual and aggregate levels.

behavioral strategies, pure coordination games

Abstract:
We study both theoretically and experimentally the decisions players make in two queueing games with batch service. In both games, players are asked to independently decide when to join a discrete-time queue to receive service, or they may simply choose not to join it at all. Equilibrium solutions in pure and mixed strategies are constructed for two games where balking is prohibited and where it is allowed. They are then tested experimentally in a study that varies the game type (balking vs. no balking) and information structure (private vs. public information) in a 2X2 between-subject design. With repeated iterations of the stage game, all four experimental conditions result in aggregate, but not individual, behavior approaching mixed-strategy equilibrium play.

Batch queueing, equilibrium solution, experimental economics

Abstract:
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

Abstract:
We focus on a class of market entry in which a newly emergent market opportunity may be fruitfully exploited by no more than a commonly known, exogenously determined number of firms. Our results show significant effects of the parameters manipulated in the study, namely, the market capacity, entry fee, and method of subject assignment to groups (fixed vs. random). In contrast to previous market entry games with linear payoff functions, we find no evidence of convergence to equilibrium play on the aggregate level. Shifting the focus of the analysis from the aggregate to the individual level, four clusters of subjects are identified. The patterns are: (1) choice of the same action that is independent of the parameters of the game or the outcome of previous presentations of the same game; (2) random choices with probabilities prescribed by the equilibrium solution for risk-neutral players; (3) random choices with probabilities equal to the individual observed overall proportion of entry; and (4) sequential dependencies that violate any model that assumes randomization. Subjects in the fourth and largest category are shown to adjust their choices in accordance with a simple principle of strategic reasoning.

Tacit Coordination, market entry game, individual behavior

Abstract:
We focus on a class of market entry in which a newly emergent market opportunity may be fruitfully exploited by no more than a commonly known, exogenously determined number of firms. Our results show significant effects of the parameters manipulated in the study, namely, the market capacity, entry fee, and method of subject assignment to groups (fixed vs. random). In contrast to previous market entry games with linear payoff functions, we find no evidence of convergence to equilibrium play on the aggregate level. Shifting the focus of the analysis from the aggregate to the individual level, four clusters of subjects are identified. The patterns are: (1) choice of the same action that is independent of the parameters of the game or the outcome of previous presentations of the same game; (2) random choices with probabilities prescribed by the equilibrium solution for risk-neutral players; (3) random choices with probabilities equal to the individual observed overall proportion of entry; and (4) sequential dependencies that violate any model that assumes randomization. Subjects in the fourth and largest category are shown to adjust their choices in accordance with a simple principle of strategic reasoning.

Abstract:
The two-person centipede game is one of the most celebrated paradoxes of backward induction in complete information extensive form games. An experimental investigation of a three-person centipede game shows that the paradoxical results are strongly affected by the size of the stakes. When the number of players in the game is increased from two to three and the game is played for unusually high stakes with group composition being randomly changed from trial to trial, the paradox is considerably weakened as players approach equilibrium play with multiple iterations of the stage game. When the game is played with low stakes, there is no evidence for equilibrium play or learning across iterations of the stage game. An adaptive learning model that assumes updating of the individual probabilities of choice outperforms alternative static and dynamic models in accounting for the major results observed in the high-stake experiment.

Game, Backward induction, experimental study, high vs. low stakes, adaptive learning

Abstract:
We study a class of trust dilemmas with symmetric players that evolve in real-time. In these games, as long as all the n players continue to cooperate, the payoff function increases exponentially over time. Simultaneously, however, the temptation to defect also increases at the same rate. The first player to defect receives the present value of the payoff function whereas each of the other n-1 players only receives a fraction d of that player's payoff. We report the results of an iterated trust dilemma that varies the values of n and d in a between-subjects design. In all cases, trust-based cooperation breaks down in the population over iterations of the stage game with the rate of breakdown sharply increasing in n and slowly decreasing in d.

Centipede game, population dynamics, cooperation, trust dilemmas

Abstract:
We study a class of trust dilemmas with symmetric players that evolve in real-time. In these games, as long as all the n players continue to cooperate, the payoff function increases exponentially over time. Simultaneously, however, the temptation to defect also increases at the same rate. The first player to defect receives the present value of the payoff function whereas each of the other n-1 players only receives a fraction d of that player's payoff. We report the results of an iterated trust dilemma that varies the values of n and d in a between-subjects design. In all cases, trust-based cooperation breaks down in the population over iterations of the stage game with the rate of breakdown sharply increasing in n and slowly decreasing in d.

Centipede game, population dynamics, cooperation, trust dilemmas

Abstract:
Disagreements between psychologists and economists about the need for and size of financial incentives continue to be hotly discussed. We examine the effects of financial incentives in a class of interactive decision making situations, called centipede games, in which mutual trust is essential for cooperation. Invoking backward induction, the Nash equilibrium solution for these games is counterintuitive. Our previous research showed that when the number of players in the centipede game is increased from two to three, the game is iterated in time, the players are re-matched, and the stakes are unusually high, behavior approaches equilibrium play. Results from the present study show that reducing the size of the stakes elicits dramatically different patterns of behavior. We argue that when mutual trust is involved the magnitude of financial incentives can induce a considerable difference.

Centipede game, backward induction, experimental study, high vs. low stakes

Abstract:
We report the results of an experiment on two-stage contests with budget-constrained agents competing to win an exogenously determined prize. We study a class of two-stage contests where in stage 1 agents first compete within their own groups by expending resources, and in stage 2 the winners of each group compete with one another to win the prize by expending additional resources subject to the budget constraint. Winners in each stage are determined by Tullock's proportional contest success function. We present the subgame perfect equilibrium solution for this model, derive predictions for our experiment, and then test them experimentally. The equilibrium model is flatly rejected mostly due to over expenditure in stage 1. A descriptive model that extends the equilibrium solution by allowing for 1) non-pecuniary utility of winning and 2) misperception of the probability of winning better accounts for some but not all of the behavioral regularities. We then turn to an adaptive learning model that accounts for several features of the dynamics of play but still significantly under-predicts the stage 1 expenditures.

Two-stage, rent-seeking, tournament, contest, EWA, experiment

Abstract:
We study a class of single-server queueing systems with a finite population size, FIFO queue discipline, and no balking or reneging. In contrast to the predominant assumptions of queueing theory of exogenously determined arrivals and steady state behavior, we investigate queueing systems with endogenously determined arrival times and focus on transient rather than steady state behavior. When arrival times are endogenous, the resulting interactive decision process is modeled as a non-cooperative n-person game with complete information. Assuming discrete strategy spaces, the mixed-strategy equilibrium solution for groups of n=20 agents is computed using a Markov chain method. Using a 2x2 between-subject design (private vs. public information by short vs. long service time), arrival and staying out decisions are presented and compared to the equilibrium predictions. The results indicate that players generate replicable patterns of behavior that are accounted for remarkably well on the aggregate, but not individual, level by the mixed-strategy equilibrium solution unless congestion is unavoidable and information about group behavior is not provided.

Queueing, experiment, large group coordination, equilibrium

Abstract:
We extend the sealed-bid k-double-auction mechanism from a single- to two-round game where offers are made simultaneously during each round. If an agreement is reached on round 1, then the traders realize their profit and the game is over. If not, equipped with information about the round 1 bids and asks, the two traders move to the second and final round. Our main hypothesis is that, if payoffs are not discounted, the traders will not bargain seriously in round 1, namely, they will reveal only limited information about their (private) reservation values. In round 2 they will play the Chatterjee-Samuelson linear equilibrium (1983). The main hypothesis is tested in an iterated game with several groups of players who differ from one another in their strategic sophistication. Our results show that strategically sophisticated players learn not to disclose information on round 1 quicker than inexperienced traders and approach linear equilibrium play on the second round of the bargaining.

Sealed-bid k-double auction, multistage, experiment, incomplete information

Abstract:
We consider mixed populations (N=21) of genuine (humans) and artificial (robots) agents, repeatedly interacting in small groups whose composition is changed randomly from round to round. Our purpose is to study the spread of cooperative or non-cooperative behavior in the population over time by manipulating the behavior of the robots (cooperative vs. non-cooperative) and their proportion in the population. Our results convey a positive message: adding a handful of cooperative robots increases the propensity of the genuine subjects to cooperate over time, whereas adding a handful of non-cooperative agents does not reduce this propensity. If there are enough persistent cooperative subjects in the population, they not only negate the non-cooperative behavior of the robots but also induce other subjects to behave more cooperatively.

Centipede game, population dynamics, cooperation, trust

Abstract:
Coordination of entry decisions in the iterated MEFC (market-entry fixed cost) game with asymmetric players and varying market capacity values can be achieved either without common knowledge of the distribution of types or without trial-to-trial information about number of entrants and individual payoff. Comparison of the results of each of the two experiments with the earlier findings reported by Rapoport, Seale and Winter (1997) shows that removing either of these two sources of information does not affect coordination on the aggregate level and possibly improves it on the type level. The Nash equilibrium solution accounts for the results of both experiments. Coordination without common knowledge is achieved by some sort of learning with players steadily increasing their use of cutoff decision rules that more or less sort themselves into types. The findings suggest that (1) providing the subjects with common knowledge of the game may not be necessary if the game is iterated for sufficiently many periods; and (2)in the absence of an opportunity to learn, players will use whatever cues they have to coordinate their actions.

Coordination, market entry, common knowledge, learning

Abstract:
The sealed-bid k-double auction mechanism for two-person bargaining under incomplete information can be extended by providing a bonus for both traders if, and only if, an agreement is reached. Brams and Kilgour (1996) proved that there is a unique level of bonus, namely, half the difference between the buyer's bid and seller's ask, that induces the traders to bargain truthfully. Stein and Parco (2001) extend the theoretical work to the case of partial bonus levels that reduce, but do not completely eliminate, misrepresentation of the reservation values. In the present study, we experimentally investigate the effects of providing different bonus values on the misrepresentation of the bargainers' reservation values. Our results show that implementation of a bonus has a significant impact on bargaining behavior but not nearly to the extent predicted by the equilibrium analysis. A reinforcement-based learning model originally proposed for the no bonus case accounts quite well for the results of all three experimental conditions.

Sealed-bid, k-double auction, bonus procedure, truthful revelation, experiment

Abstract:
We study a class of queueing problems with endogenous arrival times that we formulate as non-cooperative n-person games in normal form with discrete strategy spaces, fixed starting and closing times, and complete information. With multiple equilibria in pure strategies, these queueing games give rise to problems of tacit coordination. We first describe and illustrate a Markov chain algorithm used to compute the symmetric mixed-strategy equilibrium solution. Then, we report the results of an experimental study of a large-scale (n=20) queueing game with fixed service time, FIFO queue discipline, and no balking, reneging, and early arrivals. Our results show consistent and replicable patterns of arrival that provide strong support for mixed-strategy equilibrium play on the aggregate but not individual level.

Queueing, endogenous arrival times, mixed-strategy equilibrium, experimentation

Abstract:
We report the results of trust dilemmas that are modeled as non-cooperative n-person games evolving over time. As long as all the n players continue cooperating, their potential payoff increases exponentially over time. Simultaneously, the temptation to defect increases too, as the player who is the first to defect receives the present value of the payoff function whereas each of the other n-1 players receives only a fraction of this value. We report the results of an experiment in which population members are randomly assigned to groups on each round, and each group member specifies her stopping time before the round outcome is revealed. Our results show that when players can signal their intention to cooperate by sacrificing present earnings for possible future gain, some exercise this option. By doing so, they succeed in stopping the slow decline in the mean population cooperation level observed under the typical decision method that does not allow for signaling.

Trust dilemmas, strategy method, signaling, cooperation

Abstract:
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

Abstract:
The iterative elimination of strongly dominated strategies (IESDS) and mixed-equilibrium solution concepts are studied in an iterated two-person investment game with discrete strategy spaces, non-recoverable investments, and either equal or unequal investment capital. In this game, the player investing the largest amount wins the competition and receives a fixed reward; ties are counted as losses. Both cases of symmetric and asymmetric dyads are studied theoretically and experimentally. Results from two experiments provide support for the mixed-strategy equilibrium solution on the aggregate but not the individual level, and evidence for a hierarchy of bounded IESDS.

Keyword(s): Mixed strategies, Iterative deletion of strongly dominated strategies, Bounded rationality, Adaptive learning

Abstract:
Tacit coordination in large groups is studied in an iterated market entry game with complete information and multiple market capacities that are varied randomly from period to period. On each period, each player must decide independently whether to enter any of the markets, and if entering, which of the two markets to enter. Across symmetric and asymmetric markets, we find remarkable coordination on the aggregate level, which is accounted for by the Nash equilibrium, together with considerable individual differences in frequency of entry and decision rules. With experience, the decisions of most players converge to decision rules with cutoff values on the combined market capacity that determine whether or not to enter but not which of the two markets to enter. This latter decision is determined probabilistically by the differential market capacities. The aggregate and individual results are accounted for quite well by a reinforcement-based learning model that combines deterministic and probabilistic elements.

Market Entry Games, Coordination Success, Large Groups, Adaptive Learning, Nash Equilibrium Solution