Trust among Strangers

The trust building process is basic to social science. We investigate it in a laboratory setting using a novel multi-stage trust game where social gains are achieved if players trust each other in each stage. And in each stage, players have an opportunity to appropriate these gains or be trustworthy by sharing them. Players are strangers because they do not know the identity of others and they will not play them again in the future. Thus there is no prospect of future interaction to induce trusting behavior. So, we study the trust building process where there is little scope for social relations and networks. Standard game theory, which assumes all players are opportunistic, untrustworthy, and should have zero trust for others is used to construct a null hypothesis. We test whether people are trusting or trustworthy and examine how inferring the intentions of those who trust affects trustworthiness. We also investigate the effect of stake on trust, and study the evolution of trust. Results show subjects exhibit some degree of trusting behavior though a majority of them are not trustworthy and claim the entire social gain. Players are more reluctant to trust in later stages than in earlier ones and are more trustworthy if they are certain of the trustee’s intention. Surprisingly, subjects are more trusting and trustworthy when the stake size increases. Finally, we find the sub- population who invests in initiating the trust building process modifies its trusting behavior based on the relative fitness of trust.Experimental Economics, Behavioral Economics

Does Format of Pricing Contract Matter?

The use of linear wholesale price contract has long been recognized as a threat to achieving channel effciency. Many formats of nonlinear pricing contract have been proposed to achieve vertical channel coordination. Examples include two-part tariff and quantity discount. A two-part tariff charges the downstream party a fixed fee for participation and a uniform unit price. A quantity discount contract does not include a fixed fee and charges a lower unit price for each additional unit. Extant economic theories predict these contracts, when chosen optimally, to be revenue and division equivalent in that they all restore full channel effciency and give the same surplus to the upstream party assuming constant relative bargaining power. We conduct a laboratory experiment to test the empirical equivalence of the two pricing formats. Surprisingly, both pricing formats fail to coordinate the channel even in a well-controlled market environment with subjects motivated by significant monetary incentives. The observed channl effciencies were significantly lower than 100%. In fact, they are statistically no better than that of the linear wholesale price contract. Revenue equivalence fails because the quantity discount scheme achieves a higher channel effciency than the two-part tariff. Also, division equivalence does not hold because the quantity discount scheme accords a higher surplus to the upstream party than the two-part tariff. To account for the observed empirical regularities, we allow the downstream party to have a reference-dependent utility in which the upfront fixed fee is framed as loss andn the subsequent contribution margin as gain. The proposed model nests the standard economic model as a special case with a loss aversion coeffcient of 1.0. The estimated loss aversion coeffcient is 1.6, thereby rejecting the standard model. We rule out other plausible explanations such as parties having fairness concerns and non-linear risk attitudes.Pricing Format, Two-Part Tariff, Quantity Discount, Channel Efficiency, Double Marginalization, Reference-Dependent Utility, Experimental Economics, Behavioral Economics

Experience-weighted Attraction Learning in Normal Form Games

In ‘experience-weighted attraction’ (EWA) learning, strategies have attractions that reflect initial predispositions, are updated based on payoff experience, and determine choice probabilities according to some rule (e.g., logit). A key feature is a parameter δ that weights the strength of hypothetical reinforcement of strategies that were not chosen according to the payoff they would have yielded, relative to reinforcement of chosen strategies according to received payoffs. The other key features are two discount rates, φ and ρ, which separately discount previous attractions, and an experience weight. EWA includes reinforcement learning and weighted fictitious play (belief learning) as special cases, and hybridizes their key elements. When δ= 0 and ρ= 0, cumulative choice reinforcement results. When δ= 1 and ρ=φ, levels of reinforcement of strategies are exactly the same as expected payoffs given weighted fictitious play beliefs. Using three sets of experimental data, parameter estimates of the model were calibrated on part of the data and used to predict a holdout sample. Estimates of δ are generally around .50, φ around .8 − 1, and ρ varies from 0 to φ. Reinforcement and belief-learning special cases are generally rejected in favor of EWA, though belief models do better in some constant-sum games. EWA is able to combine the best features of previous approaches, allowing attractions to begin and grow flexibly as choice reinforcement does, but reinforcing unchosen strategies substantially as belief-based models implicitly do

Iterated dominance and iterated best response in experimental "p-beauty contests"

Picture a thin country 1000 miles long, running north and south, like Chile. Several natural attractions are located at the northern tip of the country. Suppose each of n resort developers plans to locate a resort somewhere on the country's coast (and all spots are equally attractive). After all the resort locations are chosen, an airport will be built to serve tourists, at the average of all the locations including the natural attractions. Suppose most tourists visit all the resorts equally often, except for lazy tourists who visit only the resort closest to the airport; so the developer who locates closest to the airport gets a fixed bonus of extra visitors. Where should the developer locate to be nearest to the airport? The surprising game-theoretic answer is that all the developers should locate exactly where the natural attractions are. This answer requires at least one natural attraction at the northern tip, but does not depend on the fraction of lazy tourists or the number of developers (as long as there is more than one)

A cognitive hierarchy model of games

Players in a game are “in equilibrium” if they are rational, and accurately predict other players' strategies. In many experiments, however, players are not in equilibrium. An alternative is “cognitive hierarchy” (CH) theory, where each player assumes that his strategy is the most sophisticated. The CH model has inductively defined strategic categories: step 0 players randomize; and step k thinkers best-respond, assuming that other players are distributed over step 0 through step k − 1. This model fits empirical data, and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games

A cognitive hierarchy theory of one-shot games: Some preliminary results

Strategic thinking, best-response, and mutual consistency (equilibrium) are three key modelling principles in noncooperative game theory. This paper relaxes mutual consistency to predict how players are likely to behave in in one-shot games before they can learn to equilibrate. We introduce a one-parameter cognitive hierarchy (CH) model to predict behavior in one-shot games, and initial conditions in repeated games. The CH approach assumes that players use k steps of reasoning with frequency f (k). Zero-step players randomize. Players using k (≥ 1) steps best respond given partially rational expectations about what players doing 0 through k - 1 steps actually choose. A simple axiom which expresses the intuition that steps of thinking are increasingly constrained by working memory, implies that f (k) has a Poisson distribution (characterized by a mean number of thinking steps τ ). The CH model converges to dominance-solvable equilibria when τ is large, predicts monotonic entry in binary entry games for τ < 1:25, and predicts effects of group size which are not predicted by Nash equilibrium. Best-fitting values of τ have an interquartile range of (.98,2.40) and a median of 1.65 across 80 experimental samples of matrix games, entry games, mixed-equilibrium games, and dominance-solvable p-beauty contests. The CH model also has economic value because subjects would have raised their earnings substantially if they had best-responded to model forecasts instead of making the choices they did

Experience-weighted Attraction Learning in Normal Form Games

We describe a general model, 'experience-weighted attraction' (EWA) learning, which includes reinforcement learning and a class of weighted fictitious play belief models as special cases. In EWA, strategies have attractions which reflect prior predispositions, are updated based on payoff experience, and determine choice probabilities according to some rule (e.g., logit). A key feature is a parameter δ which weights the strength of hypothetical reinforcement of strategies which were not chosen according to the payoff they would have yielded. When δ = 0 choice reinforcement results. When δ = 1, levels of reinforcement of strategies are proportional to expected payoffs given beliefs based on past history. Another key feature is the growth rates of attractions. The EWA model controls the growth rates by two decay parameters, φ and ρ, which depreciate attractions and amount of experience separately. When φ = ρ, belief-based models result; when ρ = 0 choice reinforcement results. Using three data sets, parameter estimates of the model were calibrated on part of the data and used to predict the rest. Estimates of δ are generally around .50, φ around 1, and ρ varies from 0 to φ. Choice reinforcement models often outperform belief-based models in the calibration phase and underperform in out-of-sample validation. Both special cases are generally rejected in favor of EWA, though sometimes belief models do better. EWA is able to combine the best features of both approaches, allowing attractions to begin and grow flexibly as choice reinforcement does, but reinforcing unchosen strategies substantially as belief-based models implicitly do

Store Choice and Shopping Behavior: How Price Format Works

In this paper, we present a perceived shopping utility framework for analyzing the impact of retail price format on store choice, which in turn determines three key performance metrics: (1) number of shoppers, (2) number of trips, and (3) average spending per trip. Our approach is based on the premise that when choosing a store, consumers evaluate both the fixed and variable utilities of shopping. The fixed utility does not vary from trip to trip whereas the variable utility depends on the size and composition of the shopping list. We apply our model to summarize prior findings on store choice, analyze how retailers can improve their performance, and interpret the practices of leading retailers. Our framework can also accommodate situations when retailers face multiple segments who have different sensitivities to fixed and variable utilities. Finally, we discuss recent trends (e.g., online shopping) using our approach

How Monitoring Influences Trust: A Tale of Two Faces

Monitoring changes the behavior of those who are monitored and those who monitor others. We studied behavior under different monitoring regimes in repeated trust games. We found that trustees behaved opportunistically when they anticipated monitoring—they were compliant when they knew in advance that they would be monitored, but exploited trustors when they knew in advance that they would not be monitored. Interestingly, trustors failed to anticipate how strategically their counterparts would behave. Trustors misattributed the strategic, compliant behavior they observed as signals of trustees’ trustworthiness. As a result, trustors misplaced their trust when they were unable to monitor their counterparts. We discuss the managerial implications of our results for designing and implementing monitoring systems