**Peer-reviewed articles**

‘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.

‘Market sentiments and convergence dynamics in decentralized assignment economies’ with Heinrich H. Nax, *International Journal of Game Theory*, forthcoming

In two-sided markets with transferable utility (‘assignment games’), we study the dynamics of trade arrangements and price adjustments as agents from the two market sides stochastically match, break up, and re-match in their pursuit of better opportunities. The underlying model of individual adjustments is based on the behavioral theories of adaptive learning and aspiration adjustment. Dynamics induced by this model converge to approximately optimal and stable market outcomes, but this convergence may be (exponentially) slow. We introduce the notion of a `market sentiment’ that governs which of the two market sides is temporarily more or less amenable to price adjustments, and show that such a feature may significantly speed up convergence.

**Working papers**

‘Quick or cheap? Breaking points in dynamic markets’ with Panayotis Mertikopoulos and Heinrich H. Nax

We examine two-sided markets where players arrive stochastically over time and are drawn from a continuum of types. The cost of matching a client and provider varies, so a social planner is faced with two contending objectives: a) to reduce players’ waiting time before getting matched; and b) to form efficient pairs in order to reduce matching costs. We show that such markets are characterized by a quick or cheap dilemma: Under a large class of distributional assumptions, there is no `free lunch’, i.e., there exists no clearing schedule that is simultaneously optimal along both objectives. We further identify a unique breaking point signifying a stark reduction in matching cost contrasted by an increase in waiting time. Generalizing this model, we identify two regimes: one, where no free lunch exists; the other, where a window of opportunity opens to achieve a free lunch. Remarkably, greedy scheduling is never optimal in this setting.

‘Identity and Underrepresentation’ with Jean-Paul Carvalho

We analyze economic underrepresentation as a product of identity-dependent norms. The larger a group’s representation in an economic activity (e.g. education, high-status occupation), the more the activity is deemed `appropriate’ for its members. The dynamic feedback between a group’s representation and its norms of economic participation produces more severe and robust forms of inequality than previously found. Equality of opportunity almost never results in equal outcomes, even when groups have the same productivity. Minorities and historically discriminated groups tend to be underrepresented. Glass ceilings emerge endogenously, as identity concerns cause underrepresentation to escalate at senior levels. These problems are not easily solved using standard policy tools. Identity-based quotas reduce economic output and temporary interventions are insufficient. When identities are multidimensional (e.g. race and gender), reducing underrepresentation along one identity dimension can increase underrepresentation along another. Hence the common reductionist approach of addressing inequality dimension by dimension often fails. Our results suggest that underrepresentation may be an intractable outcome of group identity.

‘The importance of memory for price discovery in decentralized markets’

with Jacob D. Leshno

We study the dynamics of price discovery in decentralized two-sided markets. There exist memoryless dynamics that converge to the core in which agents’ actions depend only on their current payoff. However, we show that for any such dynamic the convergence time can grow exponentially in the population size. We present a natural dynamic in which a player’s reservation value provides a summary of her past information and show that this dynamic converges to the core in polynomial time. In addition, the strategies implied by the dynamic are incentive compatible in a broad class of markets.

‘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.

‘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.