In Our Shoes or the Protagonist’s? Knowledge, Justification, and Projection

Sackris and Beebe (2014) report the results of a series of studies that seem to show that there are cases in which many people are willing to attribute knowledge to a protagonist even when her belief is unjustified. These results provide some reason to conclude that the folk concept of knowledge does not treat justification as necessary for its deployment. In this paper, we report a series of results that can be seen as supporting this conclusion by going some way towards ruling out an alternative account of Sackris and Beebe’s results—the possibility that the knowledge attributions that they witnessed largely stem from protagonist projection, a phenomenon in language use and interpretation in which the speaker uses words that the relevant protagonist might use to describe her own situation and the listener interprets the speaker accordingly. With that said, we do caution the reader against drawing the conclusion too strongly, on the basis of results like those reported here and by Sackris and Beebe. There are alternative possibilities regarding what drives the observed knowledge attributions in cases of unjustified true belief that must be ruled out before, on the basis of such results, we can conclude with much confidence that the folk concept of knowledge does not treat justification as necessary for its deployment

Repeated Multimarket Contact with Private Monitoring: A Belief-Free Approach

This paper studies repeated games where two players play multiple duopolistic games simultaneously (multimarket contact). A key assumption is that each player receives a noisy and private signal about the other's actions (private monitoring or observation errors). There has been no game-theoretic support that multimarket contact facilitates collusion or not, in the sense that more collusive equilibria in terms of per-market profits exist than those under a benchmark case of one market. An equilibrium candidate under the benchmark case is belief-free strategies. We are the first to construct a non-trivial class of strategies that exhibits the effect of multimarket contact from the perspectives of simplicity and mild punishment. Strategies must be simple because firms in a cartel must coordinate each other with no communication. Punishment must be mild to an extent that it does not hurt even the minimum required profits in the cartel. We thus focus on two-state automaton strategies such that the players are cooperative in at least one market even when he or she punishes a traitor. Furthermore, we identify an additional condition (partial indifference), under which the collusive equilibrium yields the optimal payoff.Comment: Accepted for the 9th Intl. Symp. on Algorithmic Game Theory; An extended version was accepted at the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20

Is Justification Necessary for Knowledge?

Justification has long been considered a necessary condition for knowledge, and theories that deny the necessity of justification have been dismissed as nonstarters. In this chapter, we challenge this long-standing view by showing that many of the arguments offered in support of it fall short and by providing empirical evidence that individuals are often willing to attribute knowledge when epistemic justification is lacking

Robert Aumann's and Thomas Schelling's Contributions to Game Theory: Analyses of Conflict and Cooperation

Advanced information on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 2005.Game Theory;

Computing Nash equilibria and evolutionarily stable states of evolutionary games

Stability analysis is an important research direction in evolutionary game theory. Evolutionarily stable states have a close relationship with Nash equilibria of repeated games, which are characterized by the folk theorem. When applying the folk theorem, one needs to compute the minimax profile of the game in order to find Nash equilibria. Computing the minimax profile is an NP-hard problem. In this paper we investigate a new methodology to compute evolutionary stable states based on the level-k equilibrium, a new refinement of Nash equilibrium in repeated games. A level-k equilibrium is implemented by a group of players who adopt reactive strategies and who have no incentive to deviate from their strategies simultaneously. Computing the level-k equilibria is tractable because the minimax payoffs and strategies are not needed. As an application, this paper develops a tractable algorithm to compute the evolutionarily stable states and the Pareto front of n-player symmetric games. Three games, including the iterated prisoner’s dilemma, are analyzed by means of the proposed methodology