We initiate the study of how auction design affects the division of surplus among bidders. We propose a parsimonious measure for equity and apply it to standard auctions for homogeneous goods. Our surplus-equitable mechanism is efficient, Bayesian-Nash incentive compatible, and achieves surplus parity among winners ex-post. The uniform-price auction is equity-optimal if and only if bidders have a common value. Against intuition, the pay-as-bid auction is not always equity-preferred if bidders have private values. In auctions with price mixing between pay-as-bid and uniform prices, we provide prior-free bounds on the equity-preferred pricing under a common regularity condition on signals. The full paper is available at https://arxiv.org/abs/2403.07799.

We propose a solution concept—satisficing equilibrium—in which each agent i does not necessarily optimize but selects one of their top ki actions in response to the actions of others. Our concept accounts for bounded rationality, which may vary across agents. We illustrate our solution concept in a number of games from the literature. We show that non-trivial satisficing equilibria may fail to exist. However, we introduce the class of approximate potential games where their existence is guaranteed and, moreover, we show that satisficing equilibrium in which all but one agent best-respond and the remaining agent plays at least a second-best action exist in asymptotically almost all games. We provide positive foundations analogous to Nash equilibrium and show that a simple dynamic converges to satisficing equilibrium in almost all large games. Moreover, we characterize satisficing equilibrium via decision theoretic axioms. Finally, we turn to the testable implications of satisficing equilibrium.

In view of the complexity of the dynamics of learning in games, we seek to decompose a game into simpler components where the dynamics' long-run behavior is well understood. A natural starting point for this is Helmholtz's theorem, which decomposes a vector field into a potential and an incompressible component. However, the geometry of game dynamics - and, in particular, the dynamics of exponential / multiplicative weights (EW) schemes - is not compatible with the Euclidean underpinnings of Helmholtz's theorem. This leads us to consider a specific Riemannian framework based on the so-called *Shahshahani metric*, and introduce the class of *incompressible games*, for which we establish the following results: First, in addition to being volume-preserving, the continuous-time EW dynamics in incompressible games admit a constant of motion and are *Poincaré recurrent* - i.e., almost every trajectory of play comes arbitrarily close to its starting point infinitely often. Second, we establish a deep connection with a well-known decomposition of games into a potential and harmonic component (where the players' objectives are aligned and anti-aligned respectively): a game is incompressible if and only if it is harmonic, implying in turn that the EW dynamics lead to Poincaré recurrence in harmonic games.

The long-run behavior of multi-agent online learning -- and, in particular, no-regret learning -- is relatively well-understood in potential games, where players have common interests. By contrast, in general harmonic games -- the strategic complement of potential games, where players have competing interests -- very little is known outside the narrow subclass of $2$-player zero-sum games with a fully-mixed equilibrium. Our paper seeks to partially fill this gap by focusing on the full class of (generalized) harmonic games and examining the convergence properties of "follow-the-regularized-leader" (FTRL), the most widely studied class of no-regret learning schemes. As a first result, we show that the continuous-time dynamics of FTRL are Poincaré recurrent, i.e., they return arbitrarily close to their starting point infinitely often, and hence fail to converge. In discrete time, the standard, "vanilla" implementation of FTRL may lead to even worse outcomes, eventually trapping the players in a perpetual cycle of best-responses. However, if FTRL is augmented with a suitable extrapolation step -- which includes as special cases the optimistic and mirror-prox variants of FTRL -- we show that learning converges to a Nash equilibrium from any initial condition, and all players are guaranteed at most $\mathcal{O}(1)$ regret. These results provide an in-depth understanding of no-regret learning in harmonic games, nesting prior work on $2$-player zero-sum games, and showing at a high level that potential and harmonic games are complementary not only from the strategic but also from the dynamic viewpoint.

Statistical discrimination results when a decision-maker observes an imperfect estimate of the quality of each candidate dependent on which demographic group they belong to [1,8]. Imperfect estimates have been modelled via noise, where the variance depends on the candidate's group ([4,6,7]). Prior literature, however, is limited to simple selection problems, where a single decision-maker tries to choose the best candidates among the applications they received.

Transaction costs are omnipresent in markets but are often omitted in economic models. We show that the presence of transaction costs can fundamentally alter incentive and welfare properties of Double Auctions, a canonical market organization. We further show that transaction costs can be categorized into two types. Double Auctions with homogeneous transaction costs---a category that includes fixed fees and price based fees---preserve the key advantages of Double Auctions without transaction costs: markets with homogeneous transaction costs are asymptotically strategyproof, and there is no efficiency-loss due to strategic behavior. In contrast, double auctions with heterogeneous transaction costs---such as spread fees---lead to complex strategic behavior (price guessing) and may result in severe market failures. Allowing for aggregate uncertainty, we extend these insights to market organizations other than Double Auctions.

We study decentralized learning dynamics for the classic assignment game with transferable utility [Shapley and Shubik 1972]. In our model agents follow an aspiration adjustment process based on their experienced payoffs (see [Sauermann and Selten 1962], [Nax and Pradelski 2014]). At random points in time firms and workers match, break up, and re-match in the search for better opportunities. Agents have aspiration levels that they adjust based on their experienced payoffs. When matched an agent occasionally tries to succeed with a higher bid than his current aspiration level. When single an agent lowers his aspiration level in the hope of attracting a partner. In particular agents 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 sentiment: 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 {polynomial time convergence}, a crucial feature from an explanatory and market design standpoint. We also show that without market sentiment the dynamic exhibits exponential time convergence. 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.