**Working papers**

‘Evolution of institutions in the medium run’ with Pierre Tarrès (2017)

The evolution of institutions and conventions is commonly modeled as a stochastic dynamical system. Stochastic stability analysis predicts the long-run stable states independent of the starting distribution when noise is vanishingly small. We complement this analysis by first deriving tight bounds on the limiting distribution for non-vanishing noise. We then show which states are *medium-run stable* and present a straightforward method to compute these states.

‘Micro influence and macro dynamics of opinion formation’ with Bernhard Clemm von Hohenberg and Michael Mäs (2017)

There is ongoing debate about the effects of social influence on the micro level and resulting opinion polarization on the macro level. We propose a general model that captures prominent, competing micro-level theories of social influence. Conducting a lab-in-the-field experiment, we observe that individual opinions shift linearly towards the mean of the distribution of other opinions. With this finding, we predict the macro-level opinion dynamics resulting from social influence. We test our predictions using data from a second lab-in-the-field experiment and find that social influence reduces opinion polarization. We corroborate these findings with additional field data.

‘Decentralized dynamics and fast convergence in the assignment game’, *University of Oxford Department of Economics Discussion Paper 700 *(2015), Extended Abstract in EC ’15 (see below)

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.

‘The dynamics of social influence’, *University of Oxford Department of Economics Discussion Paper 742 (2015)
*

Individual behavior such as smoking, fashion, and the adoption of new products is influenced by taking account of others’ actions in one’s decisions. We study social influence in a heterogeneous population and analyze the long-run behavior of the dynamics. We distinguish between cases in which social influence arises from responding to the number of current adopters, and cases in which social influence arises from responding to the cumulative usage. We identify the equilibria of the dynamics and show which equilibrium is observed in the long-run. We find that the models exhibit different behavior and hence this differentiation is of importance. We also provide an intuition for the different outcomes.

**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.

**Refereed conference articles
**

‘Decentralized dynamics to optimal and stable states in the assignment game’ with Heinrich H. Nax and H. Peyton Young, *52nd IEEE Conference on Decision and Control, *December 10-13, 2013. Florence, Italy, 2391-2397.

Payoff-driven adjustment dynamics lead to stable and optimal outcomes in decentralized two-sided assignment markets. Pairs of agents from both sides of the market randomly encounter each other and match if ‘profitable’. Very little information is available, in particular agents have no knowledge of others’ preferences, their past actions and payoffs or the value of the different matches. This process implements optimal and stable – i.e. core – allocations even though agents interact asynchronously and randomly, and there is no central authority enforcing matchings or sharing rules.

‘Decentralized dynamics and fast convergence in the assignment game’, *Proceedings of the 16th ACM Conference on Economics and Computation (EC ’15), *2015. Portland, Oregon.