‘Learning efficient Nash equilibria in distributed systems’ with H. Peyton Young, Games and Economic Behavior, 75, 882-897 (2012)
An individual’s learning rule is completely uncoupled if it does not depend directly on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient (welfare-maximizing) pure Nash equilibrium in all generic n-person games that possess at least one pure Nash equilibrium. In games that do not have such an equilibrium, there is a simple formula that expresses the long-run probability of the various disequilibrium states in terms of two factors: i) the sum of payoffs over all agents, and ii) the maximum payoff gain that results from a unilateral deviation by some agent. This welfare/stability trade-off criterion provides a novel framework for analyzing the selection of disequilibrium as well as equilibrium states in n-person games.
‘Evolutionary dynamics and equitable core selection in assignment games’ with Heinrich H. Nax, International Journal of Game Theory, 44, 4, 903-932 (2015)
We study evolutionary dynamics in assignment games where many agents interact anonymously at virtually no cost. The process is decentralized, very little information is available and trade takes place at many different prices simultaneously. We propose a completely uncoupled learning process that selects a subset of the core of the game with a natural equity interpretation. This happens even though agents have no knowledge of other agents’ strategies, payoffs, or the structure of the game, and there is no central authority with such knowledge either. In our model, agents randomly encounter other agents, make bids and offers for potential partnerships and match if the partnerships are profitable. Equity is favored by our dynamics because it is more stable, not because of any ex ante fairness criterion.
‘Core Stability and Core Selection in a Decentralized Labor Matching Market’ with Heinrich H. Nax, Games, 7, 10 (2016)
We propose a dynamic model of decentralized many-to-one matching in the context of a competitive labor market. Through wage offers and wage demands, firms compete over workers and workers compete over jobs. Firms make hire-and-fire decisions dependent on the wages of their own workers and on the alternative workers available on the job market. Workers bargain for better jobs; either individually or collectively as unions, adjusting wage demands upward/downward depending on whether they are currently employed/unemployed. We show that such a process is absorbed into the core with probability one in finite time. Moreover, within the core, allocations are selected that are characterized by surplus splitting according to a bargaining solution such that (i) firms and workforce share total revenue according to relative bargaining strengths, and (ii) workers receive equal workforce shares above their individual outside options. These results bridge empirical evidence and provide a rich set of testable predictions.
‘Decentralized dynamics and fast convergence in the assignment game’, University of Oxford Department of Economics Discussion Paper 700
We study decentralized learning dynamics for the classic assignment game with transferable utility. At random points in time firms and workers match, break up, and re-match in the search for better opportunities. We propose a simple learning process in which players have no knowledge about other players’ payoffs or actions and they update their behavior in a myopic fashion. Behavior fluctuates according to a random variable that reflects current market conditions: sometimes the firms exhibit greater price stickiness than the workers, and at other times the reverse holds. We show that this stochastic learning process converges in polynomial time to the core. While convergence to the core is known for some types of decentralized dynamics this paper is the first to prove fast convergence, a crucial feature from a practical standpoint. The proof relies on novel results for random walks on graphs, and more generally suggests a fruitful connection between the theory of random walks and matching theory.
‘Micro influence and macro dynamics of opinion formation’ with Bernhard Clemm von Hohenberg and Michael Mäs
Social media platforms, comment boards, and online market places have created unprecedented potential for social influence and resulting opinion dynamics such as polarization. We propose an encompassing model that captures competing micro-level theories of social influence. Conducting an online lab-in-the-field experiment, we observe that individual opinions shift linearly towards the mean of others’ opinions. From this finding, we predict the macro-level opinion dynamics resulting from social influence. We test our predictions using data from another lab-in-the-field experiment and find that opinion polarization decreases in the presence of social influence. We corroborate these findings with large-scale field data.
‘Efficient price discovery and information in the decentralized assignment game’
with Jacob D. Leshno
We study the dynamics of match and price discovery in decentralized assignment games. There exist naïve mechanisms that converge to the core in which agents’ actions depend only on their current payoff. However, we show that for any such mechanism the convergence time can grow exponentially in the population size. We present a natural mechanism in which a player’s reservation value provides a summary of her past information, and show that this mechanism converges to the core in polynomial time. In addition, the strategies implied by the mechanism are incentive compatible in a broad class of markets.
‘The dynamics of social influence’, University of Oxford Department of Economics Discussion Paper 742
Individual behavior such as choice of fashion, adoption of new products, and selection of means of transport is influenced by taking account of others’ actions. We study social influence in a heterogeneous population and analyze the behavior of the dynamic processes. We distinguish between two information regimes: (i) agents are influenced by the adoption ratio, (ii) agents are influenced by the usage history. We identify the stable equilibria and long-run frequencies of the dynamics. We then show that the two processes generate qualitatively different dynamics, leaving characteristic `footprints’. In particular, (ii) favors more extreme outcomes than (i).
‘Price discovery in online markets: Convergence, asymmetries and information’ with Heinrich H. Nax and Diego Nunez-Duran
Prices tend to converge rapidly to competitive prices in traditional markets for non-durable goods. An open question has been whether and why the same would apply in online markets in light of the increase in size, anonymity and information decentrality that characterizes the online setting. To address these questions we built an online trading platform to conduct controlled experiments. In terms of prices, we find that convergence does occur, but not necessarily fast. Moreover, aggregate equilibration dynamics consistently favor buyers over sellers. Regarding subjects’ individual updating behavior, we identify a simple baseline rule, whereby agents with successful bids/offers become more greedy, unsuccessful ones less. As long as the available information allows subjects to improve their `guess’ of at which price trade will occur convergence to equilibrium prices is fast. We link our empirical findings with theoretical conditions under which fast convergence is proven to occur. In addition, we provide a behavioral explanation for why price convergence typically occurs via rising prices, thus favoring in buyer-optimal prices, a phenomenon that has been observed but not explained.