One for all, all for one---von Neumann, Wald, Rawls, and Pareto

Applications of the maximin criterion extend beyond economics to statistics, computer science, politics, and operations research. However, the maximin criterion---be it von Neumann's, Wald's, or Rawls'---draws fierce criticism due to its extremely pessimistic stance. I propose a novel concept, dubbed the optimin criterion, which is based on (Pareto) optimizing the worst-case payoffs of tacit agreements. The optimin criterion generalizes and unifies results in various fields: It not only coincides with (i) Wald's statistical decision-making criterion when Nature is antagonistic, (ii) the core in cooperative games when the core is nonempty, though it exists even if the core is empty, but it also generalizes (iii) Nash equilibrium in $n$-person constant-sum games, (iv) stable matchings in matching models, and (v) competitive equilibrium in the Arrow-Debreu economy. Moreover, every Nash equilibrium satisfies the optimin criterion in an auxiliary game

On the Additivity and Weak Baselines for Search Result Diversification Research

A recent study on the topic of additivity addresses the task of search result diversification and concludes that while weaker baselines are almost always significantly improved by the evaluated diversification methods, for stronger baselines, just the opposite happens, i.e., no significant improvement can be observed. Due to the importance of the issue in shaping future research directions and evaluation strategies in search results diversification, in this work, we first aim to reproduce the findings reported in the previous study, and then investigate its possible limitations. Our extensive experiments first reveal that under the same experimental setting with that previous study, we can reach similar results. Next, we hypothesize that for stronger baselines, tuning the parameters of some methods (i.e., the trade-off parameter between the relevance and diversity of the results in this particular scenario) should be done in a more fine-grained manner. With trade-off parameters that are specifically determined for each baseline run, we show that the percentage of significant improvements even over the strong baselines can be doubled. As a further issue, we discuss the possible impact of using the same strong baseline retrieval function for the diversity computations of the methods. Our takeaway message is that in the case of a strong baseline, it is more crucial to tune the parameters of the diversification methods to be evaluated; but once this is done, additivity is achievable

Truth-telling and Trust in Sender-receiver Games with Intervention

Recent experimental studies find excessive truth-telling in strategic information transmission games with conflictive preferences. In this paper, we show that this phenomenon is more pronounced in sender-receiver games where a truthful regulator randomly intervenes. We also establish that intervention significantly increases the excessive trust of receivers.Strategic information transmission, truth-telling, trust, sender-receiver game.

Optimin achieves super-Nash performance

Since the 1990s, AI systems have achieved superhuman performance in major zero-sum games where "winning" has an unambiguous definition. However, most social interactions are mixed-motive games, where measuring the performance of AI systems is a non-trivial task. In this paper, I propose a novel benchmark called super-Nash performance to assess the performance of AI systems in mixed-motive settings. I show that a solution concept called optimin achieves super-Nash performance in every n-person game, i.e., for every Nash equilibrium there exists an optimin where every player not only receives but also guarantees super-Nash payoffs even if the others deviate unilaterally and profitably from the optimin.Comment: arXiv admin note: substantial text overlap with arXiv:1912.0021

The Effects of Comparative Advertising Format on Consumer Responses: the Moderating Effects of Brand Image and Attribute Relevance.

Comparative advertising has become a popular and powerful promotion tactic for companies competing in a highly competitive marketplace. While most research examined comparison advertisements, focusing on one brand being compared to a competitor brand, within-brand comparison advertising has been neglected. Within-brand comparison advertising compares the attributes of an extension brand with the attributes of an original or replaced brand. This dissertation examines the relative effectiveness of two forms of comparative advertising tactics, within-brand comparison versus across-brand comparison . The moderating effects of brand image and attribute relevance and the mediating effect of ad believability are also assessed by an experiment. Based on the Persuasion Knowledge Model and the Characterization-Correction Model, the results revealed that across-brand comparison ads resulted in lower ad believability, attitude toward the ad, attitude toward the brand, purchase intention, and more counterargurnents and tactics-related cognitions than within-brand comparison ads under low brand image and attribute irrelevance conditions. Interaction effects were assessed under the conditions of high brand image and attribute relevance. The findings implied that high-image brands enjoy the flexibility of using both types of comparative ads as long as they are employing relevant attributes. On the other hand, low-image brands are more likely to benefit from only within-brand comparison ads employing relevant attributes. It was also found that the within-brand comparison ads resulted in more favorable consumer responses than the across-brand comparison ads irrespective of attribute relevance. However, the results also suggest that low-image brands should prefer within-brand comparison ads to across-brand comparison ads and avoid using irrelevant attributes. Overall, within-brand comparison ads seem to result in more favorable outcomes than across-brand comparison ads while avoiding the potential risks of legal problems, competitor retaliations, and brand confusion

Mutual knowledge of rationality and correct beliefs in nn-person games: An impossibility theorem

There are two well-known sufficient conditions for Nash equilibrium: common knowledge of rationality, and common prior, which exogenously assumes a profile of beliefs that are correct. However, it is not known how players arrive at a common prior \textit{before} playing the original game. In this note, I assume, in addition to (objective and subjective) rationality, that players' beliefs \textit{will be} correct once the game is played, but a common prior is not assumed. I study whether and under what conditions players endogenously arrive at a common prior. The main finding is an impossibility theorem, which states that mutual knowledge of rationality and mutual knowledge of correct beliefs are not in general logically consistent in $n$-person games. However, the two assumptions are consistent in two-player zero-sum games