M Equilibrium: A Theory of Beliefs and Choices in Games

We introduce a set-valued solution concept, M equilibrium, to capture empirical regularities from over half a century of game theory experiments. We show M equilibrium serves as a meta theory for various models that hitherto were considered unrelated. M equilibrium is empirically robust and, despite being set-valued, falsifiable. Results from a series of experiments that compare M equilibrium to leading behavioral game theory models demonstrate its virtues in predicting observed choices and stated beliefs. Data from experimental games with a unique pure-strategy Nash equilibrium and multiple M equilibria exhibit coordination problems that could not be anticipated through the lens of existing models. (JEL C72, C90, D83)

Experience Weighted Learning in Multiagent Systems

Agents face challenges to achieve adaptability and stability when interacting with dynamic counterparts in a complex multiagent system (MAS). To strike a balance between these two goals, this paper proposes a learning algorithm for heterogeneous agents with bounded rationality. It integrates reinforcement learning as well as fictitious play to evaluate the historical information and adopt mechanisms in evolutionary game to adapt to uncertainty, which is referred to as experience weighted learning (EWL) in this paper. We have conducted multiagent simulations to test the performance of EWL in various games. The results demonstrate that the average payoff of EWL exceeds that of the baseline in all 4 games. In addition, we find that most of the EWL agents converge to pure strategy and become stable finally. Furthermore, we test the impact of 2 import parameters, respectively. The results show that the performance of EWL is quite stable and there is a potential to improve its performance by parameter optimization.

The Frequency of Convergent Games under Best-Response Dynamics

We calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of n-player, m-strategy normal-form games. To obtain the ensemble, we generate payoff matrices at random. Games with a unique pure strategy Nash equilibrium converge to the Nash equilibrium. We then consider a wider class of games that converge under a best-response dynamic, in which each player chooses their optimal pure strategy successively. We show that the frequency of convergent games with a given number of pure Nash equilibria goes to zero as the number of players or the number of strategies goes to infinity. In the 2-player case, we show that for large games with at least 10 strategies, convergent games with multiple pure strategy Nash equilibria are more likely than games with a unique Nash equilibrium. Our novel approach uses an n-partite graph to describe games.

Refinement of acyclic-and-asymmetric payoff aggregates of pure strategy efficient Nash equilibria in finite noncooperative games by maximultimin and superoptimality

A theory of refining pure strategy efficient Nash equilibria in finite noncooperative games under uncertainty is outlined. The theory is based on guaranteeing the corresponding payoffs for the players by using maximultimin, which is an expanded version of maximin. If a product of the players’ maximultimin subsets contains more than one efficient Nash equilibrium, a superoptimality rule is attached wherein minimization is substituted with summation. The superoptimality rule stands like a backup plan, and it is involved if maximultimin fails to produce just a single refined efficient equilibrium (a metaequilibrium). The number of the refinement possible outcomes is 10. There are 3 single-metaequilibrium cases, 3 partial reduction cases, and 4 fail cases. Despite successfulness of refinement drops as the game gets bigger, pessimistic estimation of its part is above 54 % for games with no more than four players.

Which Message? Which Channel? Which Customer? - Exploring Response Rates in Multi-Channel Marketing Using Short-Form Advertising

Formulating short-form advertising messages with little ad content that work and choosing high-performing channels to disseminate them are persistent challenges in multichannel marketing. Drawing on the persuasive systems design (PSD) model, we experimented with 33,848 actual customers of an international telecom company. In a real-life setting, we compared the effectiveness of three persuasion strategies (rational, emotional, and social) tested in three marketing channels (short message service (SMS), social media advertising, and mobile application), evaluating their effect on influencing customers to purchase international mobile phone credits. Results suggest that companies should send rational messages when using short-form advertising messages regardless of the channel to achieve higher response rates. Findings further show that certain customer characteristics are predictive of positive responses and differ by channel but not by message type. Findings from crowdsourced evaluations also indicate that people noticeably disagree on what persuasive strategy was applied to these short messages, indicating that consumers are not well-equipped to identify persuasive strategies or that what advertisers see as a “pure” strategy actually involves elements from multiple strategies as interpreted by consumers. The results have implications for the theoretical understanding of persuasive short-form commercial messaging in multichannel marketing and practical insights for advertising within a limited amount of space and attention afforded by many digital channels.

Numerical Solution of Asymmetric Auctions

We propose the backward indifference derivation (BID) algorithm, a new method to numerically approximate the pure strategy Nash equilibrium (PSNE) bidding functions in asymmetric first-price auctions. The BID algorithm constructs a sequence of finite-action PSNE that converges to the continuum-action PSNE by finding where bidders are indifferent between actions. Consequently, our approach differs from prevailing numerical methods that consider a system of poorly behaved differential equations. After proving convergence (conditional on knowing the maximum bid), we evaluate the numerical performance of the BID algorithm on four examples, two of which have not been previously addressed.

Benefits of Integrating an Explicit Self-Efficacy Intervention With Calculation Strategy Training for Low-Performing Elementary Students

This study examined the malleability of math self-efficacy (SE) among children with poor calculation fluency via an intervention that targeted four sources of SE (mastery experiences, vicarious experiences, social persuasions, and emotional and physiological states). The effect of pure strategy training was contrasted with an intervention that integrated strategy training and explicit SE support. Moreover, the changes in SE source experiences and their relation with math SE, as well as the relation between math-SE profiles and calculation fluency development, were examined. In a quasi-experimental design, 60 Finnish children with calculation fluency problems in Grades 2 to 4 participated in strategy training (N = 38) or in an intervention that integrated SE support with strategy training (N = 32) for 12 weeks. The results showed that the explicit SE intervention integrated with strategy training enhanced math SE among children with poor calculation fluency and low SE (effect size, r = 0.61). Changes in mastery experiences and social persuasions were positively associated with changes in math SE among children who received the explicit SE intervention. An initially high math-SE profile and a profile indicating an increase from low to high math SE were related to growth in calculation fluency that approached the children's average age level during the interventions. In conclusion, an integrated approach that combined skill training and SE intervention was especially beneficial for children with poor calculation fluency and low math SE.

Analysis of a Multiparticipant Game under a Subsidy and Punishment Mechanism: An Evolutionary Theory Perspective

In a market with intense competition, cost pressures tempt enterprises to seek profits in ways that infringe on the interests of consumers. This is especially true when market sentiment is weak. In such situations, governments play a vital role in protecting consumers’ interests and helping struggling enterprises. We construct a tripartite game model that includes the government, enterprises, and consumers under a subsidy and punishment mechanism. We use this model to investigate the strategic choices made by the participants in an evolutionary game theory (EGT) framework. We present four stable equilibrium points as pure strategy solutions with the aid of a replicator dynamic system. Three main findings are presented in this paper. First, not all equilibrium points can be evolutionary stable strategies (ESSs) when considering the potential motivations of the participants to change strategies. Second, there is an equilibrium point that satisfies the stability condition but changes periodically in its strategy space; strategy changes between participants are not synchronized. Third, the government prefers to subsidize enterprises when enterprise speculation is serious or when enterprise investment in improving production technology is high.