A three-player gambler's ruin problem: some extensions

For the expected ruin time of the classic three-player symmetric game, Sandell derived a general formula by introducing an appropriate martingale and stopping time. For the case of asymmetric game, the martingale approach is not valid to determine the ruin time. In general, the ruin probabilities for both cases, i.e. symmetric and asymmetric game and expected ruin time for asymmetric game are still awaiting to be solved for this game. The current work is also about three-player gambler’s ruin problem with some extensions as well. We provide expressions for the ruin time with (without) ties when all the players have equal (unequal) initial fortunes. Finally, the validity of asymmetric game is also tested through a Monte Carlo simulation study.

Evolutionary Game Analysis of Cross-Regional Coordinated Governance of Major Public Health Emergencies: The Example of the Spread of the COVID-19 Outbreak

Cross-regional governance of government often faces various problems, which often brings great loss to the society. The global outbreak of the novel coronavirus pneumonia (NCP) in early 2020 has not only caused serious economic and social losses to various countries but also put the current public health event governance system to a severe test. The cross-regional character and spillover effects of public health outbreak governance often make it difficult to coordinate cross-regional governance. In this context, this paper adopts a regional evolutionary game analysis framework and studies the cross-regional governance of public health emergencies by constructing a symmetric game of peripheral regions and an asymmetric game of core-peripheral regions. The marginal contribution of this paper is to attempt to construct a symmetric game model for peripheral regions and an asymmetric game model for core and peripheral regions using an evolutionary game approach to study the behavioral strategies of multiple regions in the governance of public health emergencies, and it is found that when the regional spillover effects and governance costs are small or the economic and social damages caused by public health emergencies are large, all regions will choose to conduct coordinated governance. Otherwise, there will be regions that choose to “free-ride.” This “free-rider” mentality has led to the failure in achieving good cross-regional collaborative governance of public health emergencies, resulting in a lack of efficiency in the overall governance of public health in society. However, when the spillover effect of regional governance exceeds a certain critical value, the result of the regional governance game is also the socially optimal result, when public health emergencies are effectively governed. At the same time, the relevant findings and analytical framework of this paper will provide a policy reference for the cross-regional governance of the current new crown epidemic.

Offensive, Defensive, and Generic Advertising Strategies in a Dynamic Oligopolistic Market

In today’s highly competitive business environment, advertisement plays an influential role in attracting customers and increasing market share. Companies adopt different advertising strategies in a competitive market, such as offensive, defensive, and generic, to keep and increase their market share. Researchers have generally modeled this problem using a dynamic differential game. All previous research studies have focused on finding these strategies in a duopoly market. Also, to simultaneously determine the optimal equilibrium strategy for these three strategies, the model is designed as a symmetric game due to the ease of solving. In contrast with the previous researches, the purpose of this paper is to present and solve an asymmetric game model to determine the optimal offensive, defensive, and generic advertising strategies in an oligopoly market. The proposed model’s objective is to obtain the maximum equilibrium profit for each company at any moment regarding the market share of each company and those of competitors. A numerical solution method based on the Pontryagin’s maximum principle is developed to solve the model. Then, the proposed model is solved for a triopoly market. Also, the sensitivity of the results to changes in model parameters has been investigated. The obtained results denote that in markets with more than two players under the asymmetric game, the proposed model can prescribe the optimal type of offensive, defensive, and generic advertising strategies.

Ecological Land Conservation Strategies Explained By Urban Growth and Climate Change

Rising urban population throughout the world have boosted land use demand, intensifying pressure of ecological land resources linked with climate change. By incorporating risk into assessment, people can discourage excessive growth in megacity areas. Here, we propose a generalized analysis framework of ecological land conservation by devising a public goods game, which simultaneously considers population gravity and climate change along with interactions. Our method describes strategic conservation under the growth risk of urban boundary, where recurs across multiple rounds. We find that a compact and reasonable city with spatial structure will reduces erosion risk of ecological land and the lower costs of conservation, and higher its benefits. The conservation costs at the equilibrium do not increase with the degree of emphasis on the future, which show threshold effect. Ecological lands at the city boundaries have highest eroding risk, but rather pay a disproportionate amount of cost in this asymmetric game environment, which makes controlling erosion of ecological land less sustainable. Overall, our results suggest that implementing conservation strategies will efficiently reduce aggregate damages of urban growth and mitigate climate change, otherwise it may increase increases ecological land damages substantially.

Political games of attack and defence

Political conflicts often revolve around changing versus defending a status quo . We propose to capture the dynamics between proponents and opponents of political change in terms of an asymmetric game of attack and defence with its equilibrium in mixed strategies. Formal analyses generate predictions about effort expended on revising and protecting the status quo , the form and function of false signalling and cheap talk, how power differences impact conflict intensity and the likelihood of status quo revision. Laboratory experiments on the neurocognitive and hormonal foundations of attack and defence reveal that out-of-equilibrium investments in attack emerge because of non-selfish preferences, limited capacity to compute costs and benefits and optimistic beliefs about the chances of winning from one's rival. We conclude with implications for the likelihood of political change and inertia, and discuss the role of ideology in political games of attack and defence. This article is part of the theme issue ‘The political brain: neurocognitive and computational mechanisms’.

Great Power Competition: Lessons from the Past, Implications for the Future

Throughout the 52-century long history of great power competition, human dynamics, technology, and geography are the most consequential and most permanent factors that have shaped the interaction among the great powers. This essay mines the past for lessons about great power competition by examining the structural impact of these factors on the rise and fall of great powers, the balance of power among them, and the character of their relations. In order to aid its analysis, the essay introduces three concepts that have not been discussed in the literature: 1) The system-changers: actors that are not system-makers like the great powers but have the power to change the international system and disrupt the balance of power among the system-makers.2) The strategic structure of great power competition: a structure that emerges from the interaction of the players’ preferences and determines the best strategies for the players as well as the stable outcomes of their game. The essay argues that the Thucydides Trap does not exist in the US-China rivalry because the strategic structure of this rivalry is that of either a Game of Chicken or a Peace-lover’s Dilemma. Using game theory and geopolitics, the essay is able to make long-term predictions and strategy implications for the US-China rivalry.3) The peace-lover’s dilemma: an asymmetric game whose stable outcome is the dominance of the more aggressive player (who prefers its own supremacy to sharing power with the other) over the less aggressive player (who prefers sharing power with the other to its own supremacy), hence this is a dilemma for the game’s peace-loving player.

Equilibrium Selection under the Bayes-Based Strategy Updating Rules

In this paper, first, an evolutionary game model for Bayes-based strategy updating rules was constructed, in which players can only observe a signal that reveals a strategy type instead of the strategy type directly, which deviates from the strategy type of players. Then, the equilibrium selection of populations in the case of the asymmetric game, the Battle of the Sexes (BoS), and the case of a symmetric coordination game was studied where individuals make decisions based on the signals released by each player. Finally, it was concluded that in the BoS game, when the accuracy of the signal is low, the population eventually reaches an incompatible state. If the accuracy of the signal is improved, the population finally reaches a coordinated state. In a coordination game, when the accuracy of the signal is low, the population will eventually choose a payoff-dominated equilibrium. With the improvement of signal accuracy, the equilibrium of the final selection of the population depends on its initial state.

Asymmetric collaboration in virtual reality

It has been established that Virtual Reality (VR) possesses certain qualities for educational purposes. These include the ability to place the learner at the location or in the perspective that the desired knowledge exists (e.g., travelling to another planet or shrinking to miniature size to observe internal anatomy). VR is also considered to contribute with enriching the curricular content, promoting active forms of learning, performance assessment of high validity, and provide the opportunity to teach applied academic knowledge in life-like situations. In regards to teaching mathematics and geometry, three key affordances have been identified; interactive manipulation and construction of three-dimensional geometry, comprehension of spatial relationships, and rectification of abstract problems. Safety protocols and practical guidelines from classroom experimentation have also been formulated by various research projects. In this manuscript, asymmetrical immersive VR in education will be reviewed, as it is relevant for the narrative of learning situations where multiple students use the technology together. As an example, in mathematics, asymmetric VR could be used in contexts where unknown variables must be found in collaboration. The purpose of the narrative literature review is to gain a greater understanding of how asymmetric game mechanics has influence on communication and collaboration between learners. To map the dynamics of this type of learning activity, a taxonomy will be presented. Since VR is still under development in terms of hardware and software, it is important that the current and future technical possibilities are described in a conceptual manner, as well as conclude on optimal coupling between communication dynamics and collaboration mechanics.

Asymmetric conflict: Structures, strategies, and settlement

Our target article modeled conflict within and between groups as an asymmetric game of strategy and developed a framework to explain the evolved neurobiological, psychological, and sociocultural mechanisms underlying attack and defense. Twenty-seven commentaries add insights from diverse disciplines, such as animal biology, evolutionary game theory, human neuroscience, psychology, anthropology, and political science, that collectively extend and supplement this model in three ways. Here we draw attention to the superordinate structure of attack and defense, and its subordinate means to meet the end of status quo maintenance versus change, and we discuss (1) how variations in conflict structure and power disparities between antagonists can impact strategy selection and behavior during attack and defense; (2) how the positions of attack and defense emerge endogenously and are subject to rhetoric and propaganda; and (3) how psychological and economic interventions can transform attacker-defender conflicts into coordination games that allow mutual gains and dispute resolution.