Belief-dependent motivation is important for understanding economic outcomes regarding e.g. anxiety & health, status & conformity, vengeance & wage rigidity, and guilt & contracts. The intellectual/mathematical home for describing belief-dependent motivation is an extension of traditional game theory labeled psychological game theory. My lecture will present this framework, as well as discuss how one can shed light on the empirical relevance of applications through experimental tests.
The management game "How flow can you go?" is developed to convince decision makers of international logistic providers that their current planning methods of their transportation flows may be considerably improved using OR-techniques. In fact, we have tested the game with several planners of several logistic providers and it turns out that the mathematical tool included in the management game outperforms the planners' solutions, on average, by 10%. Next, we show that cooperation among different logistic providers or between individual business units of one provider may increase profit even more. Since a fair allocation of these extra profits is essential for a successful cooperation, we use cooperative game theory methodology. More precisely, we propose the Shapley value of a cooperative game that arises from the management game as a fair allocation. Finally, the management game is illustrated by means of a case of an international logistic provider.
Risk aversion and impatience of either the bidders or the seller have been utilized to explain the popularity of buy prices in private value auctions. This paper, using a pure common value framework, models auctions with "temporary" buy prices. We characterize equilibrium bidding strategies in a general setup and then analyze a seller's incentive to post a buy price when there are two bidders. We find that, when bidders are either risk neutral or risk averse, a risk neutral seller has no incentive to post a buy price. But when the seller is risk averse, a suitably chosen buy price can raise his expected payoff when the bidders are either risk neutral or risk averse. Since expected seller revenue is lower, bidders' expected payments are likely to be lower in a common value buy-price auction. This paper thus gives a possible explanation for the popularity of buy-price auctions with both bidders and sellers.
When do people tell white lies? In this paper we distinguish between two types of white lies: those that help others at the expense of the person telling the lie, which we term altruistic white lies, and those that help both others and the liar, which we term Pareto white lies. We find a large fraction of participants are reluctant to tell even a Pareto white lie, demonstrating a pure lie aversion independent of any social preferences for outcomes. In contrast, a non-negligible fraction of participants are willing to tell an altruistic white lie that hurts them a bit but significantly helps others. Comparing white lies to those where lying increases the liar's payoff at the expense of another reveals important insights into the interaction of incentives, lying aversion, and social preferences for payoff distributions. Finally, in line with previous findings, women are less likely than men to lie when it is costly to the other side. Interestingly, we find that women are more likely to tell an altruistic lie, but tend to tell fewer Pareto lies.
It is standard in multiagent settings to assume that agents will adopt Nash equilibrium strategies. However, studies in experimental economics demonstrate that Nash equilibrium is a poor description of human players' initial behavior in normal-form games. In this paper, we consider a wide range of widely-studied models from behavioral game theory. For what we believe is the first time, we evaluate each of these models in a meta-analysis, taking as our data set large-scale and publicly-available experimental data from the literature. We then propose modifications to the best-performing model that we believe make it more suitable for practical prediction of initial play by humans in normal-form games.
We adopt a psychological games perspective to analyze behavior and beliefs in a Trust Game experiment. Subjects are randomly assigned to the role of "truster", A player, and "trustee", B player. Assuming that B subjects may be affected by guilt aversion and reciprocity, we try to elicit their belief dependent motivations with a set of hypothetical questions. We design the experiment so that subjects have no incentives to manipulate and we check that answers are reliable. We have two main treatments. In the No-Transmission (control) treatment, B's (belief dependent) preferences cannot be common knowledge, hence the game has incomplete information. In the Transmission treatment, B's answers to the hypothetical questions are transmitted and made common knowledge between the two matched subjects. In so far as such answers reveal the "psychological type" of B, this treatment approximates a psychological game with complete information. In this case, assuming that players coordinate their expectations on the efficient equilibrium, we should observe trust/cooperation when the revealed type of B is guilt averse (or reciprocal) and no-trust/defection when he is selfish. We also provide qualitative predictions for the incomplete information case, based on a simplified Bayesian psychological game. The main insight is that average behavior is intermediate. We analyze the set of answers of each B subject with a grid estimation algorithm. Most B subjects are not selfish and we observe a dominance of guilt aversion over reciprocity. Coherently with our theoretical insights, our experimental results show that in the Transmission treatment inducing a psychological game with (approximately) complete information behavior is more extreme: in the subpopulation of matched pairs where B is highly guilt averse there is more trust and cooperation than in the corresponding incomplete information setting without transmission; whereas in the subpopulation of matched pairs where B has low guilt aversion there is less trust and cooperation than in the corresponding incomplete information setting. In both information settings, we find that the B subjects' cooperation rate is positively related to guilt aversion.
We develop a numerical method for computing all pure strategy subgame-perfect equilibrium values of dynamic strategic games with discrete states and actions. We define a monotone mapping that eliminates dominated strategies, and when applied iteratively, delivers an accurate approximation to the true equilibrium payoffs of the underlying game. Our algorithm has three parts. The first provides an outer approximation to equilibrium values, constructed so that any value outside of this approximation is not an equilibrium value. The second provides an inner approximation; any value contained within this approximation is an equilibrium value. Together, the two approximations deliver a practical check of approximation accuracy. The third part of our algorithm delivers sample equilibrium paths. To illustrate our method, we apply it to a dynamic oligopoly competition with endogenous production capacity.
We introduce a new class of infinite horizon altruistic stochastic OLG model with capital and labor, but without commitment between the generations. Under mild regularity conditions, for economies with both bounded and unbounded state spaces, continuous monotone Markov perfect Nash equilibrium (MPNE) are shown to exist, and form an antichain in pointwise partial orders. Unlike existing results in related models with inelastic labor supply, these equilibrium are not necessarily Lipschitzian. For each such MPNE, we then construct corresponding stationary Markovian equilibrium invariant distributions. We then show that for many parameterizations of our economies used in applied work in macroeconomics, unique MPNE exist relative to a large space of pure strategy equilibrium (i.e., the space of bounded measurable functions). Using this result, we can directly relate this result to the promised utility/continuation methods based upon the work of Abreu, Pearce, and Stacchetti. As our results are constructive, we can provide characterizations of numerical methods for the uniform approximation of MPNE, and we construct error bounds for simple discretization methods. Decentralizing MPNE in the game as a recursive competitive equilibrium is discussed. Finally, a series of examples show potential applications and limitations of our results.
I study a many-to-many, two-sided, transferable-utility matching game. Consider data on matches or relationships between agents but not on the choice set of each agent. I investigate what economic parameters can be learned from data on equilibrium matches and agent characteristics. Features of a production function, which gives the surplus from a match, are nonparametrically identified. In particular, the ratios of complementarities from multiple pairs of inputs are identified. Also, the ordering of production levels is identified.
We examine repeated games played among members of a society who are connected in a social network. Players can observe each others' play, but can only directly affect the payoffs of their social neighbors. We characterize the social network patterns that sustain repeated cooperative equilibrium behavior and are robust in various ways. High levels of cooperation can only be sustained as robust equilibria in specific sorts of social networks, and so analyzing repeated games can have strong implications for how social network structure affects its members' behaviors and welfare.
I develop a dynamic heterogeneous agents model of strategic network formation, where a matching technology and preferences for same-type individuals drive the dynamics of friendship. The model converges to a unique stationary distribution that is structurally estimated using Markov Chain Monte Carlo methods and stochastic approximation techniques. I use data from the restricted version of Add Health, a representative survey of US high schools containing detailed data on the actual friendship network of each student. Results show that the tendency to create links to individuals of the same racial group is pervasive. However, I find that a certain degree of heterogeneity in mutual and indirect friends increases utility of the agents. I use the model to simulate policies whose goal is to increase the degree of interracial contact. I re-assign some minority students to another school where there are only few minority students. The simulations show that these policies decrease students' welfare in the new stationary equilibrium.
eBay's Buy It Now format allows a seller to list an auction with a "buy price" at which a bidder may purchase the item immediately and end the auction. When values are common, there is theoretically no revenue advantage to offering a buy price whether bidders are risk neutral or risk averse, while when values are private a buy price can be advantageous for the seller when bidders are risk averse. We report the results of laboratory experiments designed to determine whether in practice a buy price is advantageous to the seller. We find that a suitably chosen buy price yields a substantial increase in seller revenue when values are private, and a small (but statistically insignificant) increase in revenue when values are common. In both cases a buy price reduces the variance of seller revenue. A behavioral model which incorporates the winner's curse and the overweighting by bidders of their own signal explains the common value auction data better than the rational model.
In some situations, players have to start analyzing the game before they have formed their preferences over the outcomes of the game. However, strategic analysis naturally depends on preferences. This dilemma will be discussed and some ideas for resolving it will be presented.
The multi-location replenishment and transshipment problem is concerned with several retailers facing random demand for the same item at distinct markets, that may use transshipments to eliminate excess inventory/shortages after demand realization. When the system is decentralized so that each retailer operates to maximize their own profit, there are incentive problems that prevent coordination. These problems arise even with two retailers who may pay each other for transshipped units. We propose a new mechanism based on a transshipment fund which is the first to coordinate the system, in a fully non-cooperative setting, for all instances of two retailers as well as all instances of any number of retailers. Moreover, our mechanism strongly coordinates the system, i.e., achieves coordination as the unique equilibrium. The computation and information requirements of this mechanism are realistic and relatively modest. We also present necessary and sufficient conditions for coordination and prove they are always satisfied with our mechanism. Numerical examples illustrate some of the properties underlying this mechanism for two retailers.
Motivated by online matching marketplaces such as social lending, we study markets where capacity-constrained bidders participate in multiple auctions that they have preferences over. While bidders have explicit preferences over auctions, we observe that the auctioneer side of the market has implicit preferences over bidders induced by the bids; this allows us to model these marketplaces in a matching framework with two-sided preferences. The problem of clearing the market leads naturally to the algorithmic question of computing Pareto-optimal stable matchings in a many-to-many setting with ties and incomplete lists. We will provide a fast algorithm for computing Pareto-stable assignments for this very general multi-unit matching problem with arbitrary preference lists on both sides, with running time that is polynomial in the number of agents in the market, rather than the sum of capacities of all agents.
As internet retailing has become increasingly prevalent, firms have continued to innovate by adopting multi-channel strategies. One of these innovations is the introduction of a distribution channel, commonly known as site-to-store or online-to-store, where consumers can purchase online and pick up in-store. In this project, our focus is on understanding the effects of the site-to-store channel on the retailer's pricing strategy, profitability, and demand realization.
This paper characterizes the communication networks (directed graphs) for which, in any environment (utilities and beliefs), every incentive compatible social choice function is implementable. We show that any incentive compatible social choice function is implementable on a given communication network, in all environments with either common independent beliefs and private values or a worst outcome, if and only if the network is strongly connected and weakly 2-connected. A network is strongly connected if for each player, there exists a directed path to the designer. It is weakly 2-connected if each player is either directly connected to the designer or indirectly connected to the designer through two disjoint paths not necessarily directed. We couple encryption techniques together with appropriate incentives to secure the transmission of each player's private information to the designer.
The talk will be an overview of mechanisms for the one-sided matching problem, also called the house-allocation problem. This and related problems serve as useful models for many allocation problems that arise in practice: prominent recent examples include organizing kidney exchanges and assigning students to schools. We'll briefly discuss these applications, and discuss a recent result that establishes the equivalence of a broad class of mechanisms to the uniform lottery mechanism (also called the random priority mechanism).
