Nash Equilibrium Predictions Research Articles

Assignment markets: Theory and experiments

We experimentally test convergence to the core in two-sided markets for heterogeneous indivisible goods under different trading institutions. We use bargaining and strategic games as predictors that naturally generalize the core, accommodating non-equilibrium behavior. The performance of the competing theories reflects the differences in trading procedures—market outcomes are close to Nash equilibrium predictions under auction-like institutions and close to bargaining for institutions that feature decentralized negotiations. This difference may be driving the documented effect of fewer no-trade outcomes at the expense of a higher chance of suboptimal match under free-form bargaining.

Rent dissipation and streamlined costs: Laboratory experiments

The effect of group size and effort cost on rent dissipation in the standard Tullock rent seeking model is examined using a laboratory experiment. Data support qualitative comparative static Nash equilibrium predictions as reductions in both group size and effort cost increase effort levels. However, effort and dissipation rates are above Nash predictions for all treatments. In addition, while cutting per-unit effort costs in half increases individual effort levels, they do not fully double as predicted and therefore lower rent dissipation, creating a policy-relevant “streamlining effect”. A quantal response equilibrium, which adds stochastic elements into the game structure, predicts the observed higher effort levels and dissipation but is proven to be unable to explain the streamlining effect. A modification of quantal response that incorporates implementation error noise and loss aversion outperforms other estimated models and tracks the observed all data patterns more closely, including the streamlining effect.

Bilateral Conflict: An Experimental Study of Strategic Effectiveness and Equilibrium

AbstractBilateral conflict involves an attacker with several alternative attack methods and a defender who can take various actions to better respond to different types of attack. These situations have wide applicability to political, legal, and economic disputes, but they are particularly challenging to study empirically because the payoffs are unknown. Moreover, each party has an incentive to behave unpredictably, so theoretical predictions are stochastic. This article reports results of an experiment where the details of the environment are tightly controlled. The results sharply contradict the Nash equilibrium predictions about how the two parties’ choice frequencies change in response to the relative effectiveness of alternative attack strategies. In contrast, nonparametric quantal response equilibrium predictions match the observed treatment effects. Estimation of the experimentally controlled payoff parameters across treatments accurately recovers the true values of those parameters with the logit quantal response equilibrium model but not with the Nash equilibrium model.

Learning in rent-seeking contests with payoff risk and foregone payoff information

We test whether deviations from Nash equilibrium in rent-seeking contests can be explained by the slow convergence of payoff-based learning. We identify and eliminate two noise sources that slow down learning: first, opponents are changing their actions across rounds; second, payoffs are probabilistic, which reduces the correlation between expected and realized payoffs. We find that average choices are not significantly different from the risk-neutral Nash equilibrium predictions only when both noise sources are eliminated by supplying foregone payoff information and removing payoff risk. Payoff-based learning can explain these results better than alternative theories. We propose a hybrid learning model that combines reinforcement and belief learning with risk, social and other preferences, and show that it fits data well, mostly because of reinforcement learning.

Random Actions in Experimental Zero-Sum Games

A mixed strategy, a strategy of unpredictable actions, is applicable to business, politics, and sports. Playing mixed strategies, however, poses a challenge, as the game theory involves calculating probabilities and executing random actions. I test i.i.d. hypotheses of the mixed strategy Nash equilibrium with the simplest experiments in which student participants play zero-sum games in multiple iterations and possibly figure out the optimal mixed strategy (equilibrium) through the games. My results confirm that most players behave differently from the Nash equilibrium prediction for the simplest 2x2 zero-sum game (matching-pennies) and 3x3 zero-sum game (e.g., the rock-paper-scissors game). The results indicate the need to further develop theoretical models that explain a non-Nash equilibrium behavior.

Overcoming Cost Disadvantages in Procurement Auctions

ABSTRACTAn increasingly studied auction format is the asymmetric procurement auction, which features an advantaged bidder selling a good or service to a buyer. Such asymmetric setups, although generally believed to be more realistic, are also more complex. We investigate one such setting where one bidder has a cost advantage. Our central question is whether bidders who are cost disadvantaged can overcome their inferior cost position. In a design that mirrors real construction procurement auctions, our laboratory experiment tests whether two information asymmetries (more precise cost estimates and knowledge about the cost estimating abilities of a competitor) allow cost‐disadvantaged sellers to better compete. We begin by testing bidder performance in a procurement auction where the only asymmetry is due to a cost. In this setting, analytical benchmarks are known. We find—consistent with other studies—that all bidder types submit aggressive bids well below the Nash equilibrium predictions. Over time, subjects submit less aggressive bids, moving closer to what theory would predict. We then extend our experiments to include our novel, multiple asymmetry setup. We find that endowing cost‐disadvantaged bidders with higher cost estimate precision benefits the bidder, as one might expect. Notably, providing market knowledge about a rival's ability to estimate costs may not provide a benefit; in fact, it seems bidders are not able to use this information effectively and performance suffers. Finally, we show how bidders behave myopically when making these decisions. These implications raise important questions about how asymmetries interact in complex auction settings.

Overcoming Cost Disadvantages in Procurement Auctions

An increasingly studied auction format is the asymmetric procurement auction, which features an advantaged bidder selling a good or service to a buyer. Such asymmetric setups, while generally believed to be more realistic, are also more complex. We investigate one such setting where one bidder has a cost advantage. Our central question is whether bidders who are cost-disadvantaged can overcome their inferior cost position. In a design that mirrors real construction procurement auctions, our laboratory experiment tests whether two information asymmetries (more precise cost estimates and knowledge about the cost estimating abilities of a competitor) allow cost-disadvantaged sellers to better compete. We begin by testing bidder performance in a procurement auction where the only asymmetry is due to a cost. In this setting, analytical benchmarks are known. We find – consistent with other studies – that all bidder types submit aggressive bids well below the Nash equilibrium predictions. Over time, subjects submit less aggressive bids, moving closer to what theory would predict. We then extend our experiments to include our novel, multiple asymmetry setup. We find that endowing cost-disadvantaged bidders with higher cost estimate precision benefits the bidder, as one might expect. Notably, providing market knowledge about a rival’s ability to estimate costs may not provide a benefit; in fact, it seems bidders are not able to use this information effectively and performance suffers. Finally, we show how bidders behave myopically when making these decisions. These implications raise important questions about how asymmetries interact in complex auction settings.

The Commitment Conundrum of Inventory Sharing

Motivated by the emergence of the Internet‐enabled inventory sharing across firms, we investigate different commitment scenarios of decentralized inventory sharing platforms, through a behavioral lens. In particular, we consider two transfer price commitment settings ( ex ante or ex post depending on whether or not the inventory transfer price is committed before demand realization) and two sharing commitment rules ( automatic or voluntary depending on whether or not inventory sharing are pre‐committed). Our experimental results suggest that individuals set transfer prices much lower, and order much less, than what Nash equilibrium predicts. We also find substantial treatment effects that the rational model cannot explain. The magnitude of disparities relative to the Nash equilibrium prediction appears to be most substantial in the situation where transfer price is set ex ante (i.e., transfer price commitment) and inventory sharing is voluntary (i.e., no sharing commitment). Motivated by these observations, we develop a behavioral model that incorporates quantal response equilibrium and fairness concerns. Empirical analysis indicates that our model provides a compelling explanation of the behavior observed in the data. This study provides implication on the design of the commitment rules in decentralized inventory‐sharing platforms. Specifically, in order to gain the most benefit from inventory sharing, parties should either postpone the decision of transfer price until the need for sharing arises, or pre‐commit to sharing.

Behavioral Modeling of Inventory Sharing Among Decentralized Retailers: An Experimental Study

In recent years, inventory sharing, in addition to the traditional within-firm model, also appears in the sharing-economy model where different firms can share their inventory via an internet platform. Two prominent issues, shaping the behaviors of inventory sharing systems, are the commitment of the transfer price and the commitment to share. In this paper we investigate, through a behavioral lens, the decisions of transfer price, order quantity and the resulting supply chain efficiency in different transshipment commitment scenarios. In particular, we consider two transfer price commitment settings (ex-ante or ex-post, depending on whether or not the inventory transfer price is committed before demand realization) and two sharing commitment rules (automatic or voluntary, depending on whether or not inventory sharing are pre-committed). Our experimental results suggest that individuals set transfer prices much lower, and order much less, than what Nash equilibrium predicts. We also find substantial treatment effects where rational model can not explain. The magnitude of disparities relative to the Nash equilibrium prediction appears to be most substantial in the situation where transfer price is set ex ante and inventory sharing is voluntary. Motivated by these observations, we develop a behavioral model that incorporates quantal response equilibrium and fairness concerns. Empirical analysis indicates that our model provides a compelling explanation of the behavior observed in the data. This study provides implication on the design of the commitment rules in decentralized inventory sharing platforms.

Information aggregation and turnout in proportional representation: A laboratory experiment

This paper documents a laboratory experiment that analyzes voter participation in common interest proportional representation (PR) elections, comparing this with majority rule. Consistent with theoretical predictions, poorly informed voters in either system abstain from voting, thereby shifting weight to those who are better informed. A dilution problem makes mistakes especially costly under PR, so abstention is higher in PR in contrast with private interest environments, and welfare is lower. Deviations from Nash equilibrium predictions can be accommodated by a logit version of quantal response equilibrium (QRE), which allows for voter mistakes.

Oligopolistic quantity competition with bounded rationality and social comparison

We study sales quantity competition among multiple sellers, through a combination of laboratory experiments and theoretical analyses. We conduct laboratory experiments with a 2×2 design from two dimensions: the procurement cost and the number of sellers. The experimental data eloquently exhibit bell-shaped distributions over all alternatives, with peak values consistently larger than the classical Nash equilibrium predictions. We propose a behavioral model which incorporates the behavioral elements of bounded rationality and social comparison, as well as time trends (the learning process). We derive several useful equilibrium properties of the model. The structural estimations show that the proposed behavioral model can effectively explain the experimental data.

Rationalizing (Non-)equilibrium Bidding in Maximum-Value Auctions Without Beliefs About Others’ Behavior

We propose a novel approach to the modelling of second-price Maximum-Value auctions that assumes no belief about others’ behavior and no expected profit maximization. This individual decision-making model, naive Impulse Balance Equilibrium or nIBE, deals with bidders’ anticipated regrets from winning and from losing the auction. It exploits the stochastic properties of the auction format and rationalizes: (i) Nash equilibrium bidding, (ii) (non-)monotone overbidding and (iii) fully cursed equilibrium bidding. We fit this model to the available data and find that it explains median bids better than the Nash equilibrium prediction and, overall, as well as cursed-equilibrium. Furthermore, nIBE and the noise-free variant of cursed equilibrium typically outperform HQRE models with level-k or cursed equilibrium beliefs in terms of in- and out-of-sample quartile predictions.

Exploration vs Exploitation, Impulse Balance Equilibrium, and a Specification Test for the El Farol Bar Problem

The paper reports on market-entry experiments that manipulate both payoff structures and payoff levels to assess two stationary models of behaviour: Exploration vs Exploitation (EvE, which is equivalent to Quantal Response Equilibrium) and Impulse Balance Equilibrium (IBE). These models explain the data equally well in terms of goodness-of-fit whenever the observed probability of entry is less than the symmetric Nash equilibrium prediction; otherwise IBE marginally outperforms EvE. When assuming agents playing symmetric strategies, and estimating the models with session data, IBE yields more theory-consistent estimates than EvE, no matter the payoff structure or level. However, the opposite occurs when the symmetry assumption is relaxed. The conduct of a specification test rejects the validity of the restrictions on entry probabilities imposed by EvE for agents with symmetric strategies, in 50 to 75% of sessions and it always rejects it in the case of IBE, which indicates that the symmetric variant of these models has little empirical support.

Valuation structure in incomplete information contests: experimental evidence

We experimentally examine perfectly discriminating contests under three valuation structures: pure common-value, pure private-value and a case with both private and common value components. In line with the results from the previous literature, we find that, regardless of valuation structure, contestants often choose very conservative expenditures, and very aggressive expenditures. Average expenditures exceed Nash equilibrium predictions. In valuation structures with a common value component, contestants often choose expenditures in excess of the expected value of the prize conditional on winning the contest. That is, they often guarantee themselves negative payoffs in expectation.

Community Level Natural Resource Management Institutions Work in (Game) Theory as Well as in Practice: Lottery Allocation of Fishing Sites Implements Correlated Equilibrium

The Institutional Analysis and Development (IAD) literature led by Elinor Ostrom concludes that Nash equilibrium predictions are empirically falsified in the social dilemmas found in community-level natural resource management problems. However, Nash equilibrium is not the only solution concept within noncooperative game theory. Here we demonstrate the power of Correlated Equilibrium (CE) to explain lotteries for the allocation of fishing sites as enduring community-level natural resource management institutions. Such CE-implementing lotteries are procedurally fair, equitable, and increase total expected fishery value. This modeling approach also reveals the nature of the interdependence between the size and spacing of fishing sites and the in-use characteristics of fishing gear on the one hand, and the degree of formalization of property rights and the structural features of the natural resource management institution on the other hand. When appropriately applied, noncooperative game theory offers a powerful explanatory complement to the IAD literature on community-level natural resource management.

Community-level natural resource management institutions: A noncooperative equilibrium example

The Institutional Analysis and Development (IAD) literature finds that Nash equilibrium predictions are empirically falsified in the social dilemmas that arise in community-level natural resource management problems. However, Nash equilibrium is not the only solution concept within noncooperative game theory. Here we demonstrate the power of Correlated Equilibrium (CE) to explain lotteries for the allocation of fishing sites as enduring community-level natural resource management institutions. Such CE-implementing lotteries are procedurally fair, equitable, and increase total expected fishery value.This modeling approach clarifies two further sets of relationships. It reveals the nature of the interdependence between the size and spacing of fishing sites and (a) the in-use characteristics of fishing gear, as well as (b) the degree of formalization of property rights and the structural features of the natural resource-management institution. When appropriately applied, noncooperative game theory offers a powerful explanatory complement to the IAD literature on community-level natural resource management.

Exploration vs Exploitation, Impulse Balance Equilibrium, and a Specification Test for the El Farol Bar Problem

The paper reports on market-entry experiments that manipulate both payoff structures and payoff levels to assess two stationary models of behaviour: Exploration vs Exploitation (EvE, which is equivalent to Quantal Response Equilibrium) and Impulse Balance Equilibrium (IBE). These models explain the data equally well in terms of goodness-of-fit whenever the observed probability of entry is less than the symmetric Nash equilibrium prediction; otherwise IBE marginally outperforms EvE. When assuming agents playing symmetric strategies, and estimating the models with session data, IBE yields more theory-consistent estimates than EvE, no matter the payoff structure or level. However, the opposite occurs when the symmetry assumption is relaxed. The conduct of a specification test rejects the validity of the restrictions on entry probabilities imposed by EvE for agents with symmetric strategies, in 50 to 75% of sessions and it always rejects it in the case of IBE, which indicates that the symmetric variant of these models has little empirical support.

Yes, I'll Do it: A Large-Scale Experiment on the Volunteer's Dilemma

In many real-life situations people face a simple decision whether to volunteer or not to provide some benefit for themselves and also for others. This research investigates the effects of the group size and the magnitude of the volunteering cost in a controlled large-scale laboratory experiment, where subjects play the volunteer’s dilemma only once. The experiment varies group sizes ranging from groups of 3 to about 100, and 2 different cost/benefit ratios. Results show that high cost reduces volunteering probability only in the smallest groups, but not for other group sizes. Furthermore, non-monotonic group size effect is found on the individual volunteering decisions. These findings are not in line with the mixed-strategy Nash equilibrium prediction. Subjects volunteer more often in most treatments than the Nash prediction which benefits them on average compared to the Nash prediction.

Behavioral Heterogeneity Affects Individual Performances in Experimental and Computational Lowest Unique Integer Games

This study computationally examines (1) how the behaviors of subjects are represented, (2) whether the classification of subjects is related to the scale of the game, and (3) what kind of behavioral models are successful in small-sized lowest unique integer games (LUIGs). In a LUIG, N (>= 3) players submit a positive integer up to M(> 1) and the player choosing the smallest number not chosen by anyone else wins. For this purpose, the author considers four LUIGs with N = {3, 4} and M = {3, 4} and uses the behavioral data obtained in the laboratory experiment by Yamada and Hanaki (Physica A 463, pp. 88–102, 2016). For computational experiments, the author calibrates the parameters of typical learning models for each subject and then pursues round robin competitions. The main findings are in the following: First, the subjects who played not differently from the mixed-strategy Nash equilibrium (MSE) prediction tended to made use of not only their choices but also the game outcomes. Meanwhile those who deviated from the MSE prediction took care of only their choices as the complexity of the game increased. Second, the heterogeneity of player strategies depends on both the number of players (N) and the upper limit (M). Third, when groups consist of different agents like in the earlier laboratory experiment, sticking behavior is quite effective to win.

Communication Among Voters Benefits the Majority Party

How does communication among voters affect turnout? And who benefits from it? In a laboratory experiment in which subjects, divided into two competing parties, choose between costly voting and abstaining, we study three pre-play communication treatments: No Communication, a control; Public Communication, where all voters exchange public messages through computer chat; and Party Communication, where messages are also exchanged but only within one's own party. Our main finding is that communication always benefits the majority party by increasing its expected turnout margin and, hence, its expected margin of victory and probability of winning the election. Party communication increases overall turnout, while public communication increases turnout with a high voting cost but decreases it with a low voting cost. With communication, we find essentially no support for the standard Nash equilibrium predictions and limited consistency with correlated equilibrium.