Jörgen Weibull

A new solution concept for finite games is presented and analyzed. It is defined in terms of outcomes—probability distributions over the plays of the game. Solid outcomes are robust to the representation of the game, whether in normal or extensive form, and are consistent with backward induction. They are also unaffected by the removal or addition of dominated strategies. Solid outcome sets exist in all finite extensive-form games with perfect recall. They have support in minimal “game blocks,” a class of product sets of pure-strategy profiles that are robust set-valued candidates for conventions and social norms in recurrent population play of the game. Algorithms for identifying all solid outcomes are presented, and simulations illustrate the solution concept's significant cutting power and computational efficiency.

Greater knowledge is always an advantage for a rational individual. However, this article shows that for a group of rational individuals greater knowledge can backfire, leading to a worse outcome for all. Surprisingly, this can happen even when new knowledge does not mean the discovery of a new action but simply provides a deeper understanding of the interaction at stake. More specifically, enhanced knowledge about the current state of nature may hinder cooperation among purely self-interested individuals. The paper describes this paradoxical possibility—a ‘knowledge curse’—and analyses the evolutionary process that occurs if, initially, only a few people have access to the greater knowledge. It concludes with a tentative comment on ways to avert this potential knowledge backlash.

Theorem 1 in Alger and Weibull (2016, Games and Economic Behavior) consists of two statements. The first establishes that Homo moralis with the right degree of morality is evolutionarily stable. The second statement is a claim about sufficient conditions for other goal functions to be evolutionarily unstable. However, the proof given for that claim presumes that all relevant sets are non-empty, while the hypothesis of the theorem does not guarantee that. We here prove instability under a stronger hypothesis that guarantees existence, and we also establish a new and closely related result. As a by-product, we also obtain an extension of Theorem 1 in Alger and Weibull (2013, Econometrica).

We analyze equilibrium outcomes under costly screening of candidates from distinct categories. Candidates choose how much effort to invest in skill acquisition, and the screener decides how carefully to screen each candidate. Typically, there are multiple equilibria, and ex ante identical individuals in different categories can receive different equilibrium treatment. The imposition of a quota for an initially disadvantaged group can result in increased screening intensity and skill investment by destabilizing the least active equilibrium. The endogeneity of screening enables powerful comparative statics, which we use to unify different strands in the literature on discrimination.

We analyze a principal-agent model with moral hazard where the principal is risk neutral while the agent is risk averse or risk neutral. The agent is free to choose any probability distribution over outcomes, where some distributions require more effort than others. The agent's effort-cost function is of “Legendre type” and satisfies an axiom of invariance under mergers of outcomes that are equally paid by the principal. We analyze a family of such effort-cost functions. For a canonical subclass of these, and arbitrary outcome spaces, the principal's contract problem allows for closed-form solutions. Optimal contracts then combine debt with a monotonic sharing rule for the surplus above a threshold chosen by the principal. When the agent is risk neutral, the contract boils down to a pure debt contract. For agents with unit degree of relative risk aversion, the surplus is divided in fixed shares.

Nonpharmaceutical interventions (NPIs) such as mask wearing can be effective in mitigating the spread of infectious diseases. Therefore, understanding the behavioral dynamics of NPIs is critical for characterizing the dynamics of disease spread. Nevertheless, standard infection models tend to focus only on disease states, overlooking the dynamics of "beneficial contagions," e.g., compliance with NPIs. In this work, we investigate the concurrent spread of disease and mask-wearing behavior over multiplex networks. Our proposed framework captures both the competing and complementary relationships between the dueling contagion processes. Further, the model accounts for various behavioral mechanisms that influence mask wearing, such as peer pressure and fear of infection. Our results reveal that under the coupled disease-behavior dynamics, the attack rate of a disease-as a function of transition probability-exhibits a critical transition. Specifically, as the transmission probability exceeds a critical threshold, the attack rate decreases abruptly due to sustained mask-wearing responses. We empirically explore the causes of the critical transition and demonstrate the robustness of the observed phenomena. Our results highlight that without proper enforcement of NPIs, reductions in the disease transmission probability via other interventions may not be sufficient to reduce the final epidemic size

How much and when should we limit economic and social activity to ensure that the health-care system is not overwhelmed during an epidemic? We study a setting where ICU resources are constrained while suppression is costly (e.g., limiting economic interaction). Providing a fully analytical solution we show that the common wisdom of "flattening the curve", where suppression measures are continuously taken to hold down the spread throughout the epidemic, is suboptimal. Instead, the optimal suppression is discountinuous. The epidemic should be left unregulated in a first phase and when the ICU constraint is approaching society should quickly lock down (a discontinuity). After the lockdown regulation should gradually be lifted, holding the rate of infected constant thus respecting the ICU resources while not unnecessarily limiting economic activity. In a final phase, regulation is lifted. We call this strategy "filling the box". * We wish to thank Tommy Andersson, Hannes Malmberg and Robert Östling for valuable comments.

A model of the dynamics of distributions of individual wealth, or of individual Darwinian fitness, is here developed. Pairs of individuals are recurrently and randomly matched to play a game over a resource. In addition, all individuals have random access to a constant background source, and their fitness or wealth depreciates over time. For brevity, we focus on the wellknown Hawk-Dove game. In the base-line model, the probability of winning a fight over a resource is the same for both parties. In an extended version, the individual with higher current fitness or wealth has a higher probability of winning. Analytical results are given for the fitness/wealth distribution at any given time, for the evolution of average fitness/wealth over time, and for the asymptotics with respect to both time and population size. Long-run average fitness/wealth is non-monotonic in the value of the resource, thus providing a potential explanation of the so-called curse of the riches.

We analyze a principal-agent model with moral hazard where the principal is risk neutral and the agent is risk averse or risk neutral. The agents' actions determine the probability distribution over outcomes, where some probability distributions require more effort than others. We analyze a family of effort disutility functions with arguably desirable properties. For a canonical class of such functions and arbitrary outcome spaces, the model is explicitly solvable. Optimal contracts combine debt with a monotonic sharing rule for the surplus created. When the agent is risk neutral, the contract is a pure debt contract. For agents with unit degree of relative risk aversion, the surplus is divided in fixed shares