Continuous Games Research Articles

Between God and Caesar: The Catholic Bishops’ Election and Consecration in China

The appointment of Chinese bishops of the Catholic Church is generally considered as the biggest obstacle in the normalization of diplomatic relations between China and the Vatican. However, due to the special nature of the identity and status of Catholic bishops, there are continuous confrontations and gaming between the Vatican and the Chinese Government as well as its religious administrative department, manifested as confrontations between religious social groups and the administrative power, between the principle of Catholic hierarchy and the principle of independence and autonomy in the self-management of the Church. The root of these confrontations lies in the competition for the leadership and appointment of future Catholic Church leaders. Therefore, in this context, the state–society relationship is strained, as reflected by the interactions between the Catholic Church in China and the government. The Catholic Church is faced with a choice between God and Caesar. Such a situation, even if China and the Vatican could reach an agreement on the appointment of bishops, will not change and confrontations are likely to occur.

Evolution of stinginess and generosity in finite populations

In iterated continuous games, the cooperative investment in a given round is determined by the initial investment and the reciprocation rate, which describe the investment in the first round and the dependence of current investment on the partner’s last move, respectively. These two traits usually intertwine during evolution. However, their coevolution is not fully explored. In this paper, we thereby study their coevolution in the iterated continuous public goods games. We find that the reciprocation rate plays a dominant role during the coevolution in both finite and infinite populations. If it exceeds a threshold, a stingy population where individuals invest no more than their partner’s last investment evolves to full cooperation, and a generous population where individuals invest more than their partner’s last investment decreases to a moderate cooperative state, investing a portion in the first round and then escalating investment in the following rounds. Otherwise, the stingy population evolves to full defection, and the generous one rises to another moderate cooperative state.

Repeated Bidding Games with Incomplete Information and Bounded Values: On the Exponential Speed of Convergence

We consider the repeated zero-sum bidding game with incomplete information on one side with non-normalized total payoff. De Meyer and Marino [(2005) Continuous versus discrete market game, Cowles Foundation Discussion Paper 1535] and Domansky and Kreps [(2005) Repeated games with asymmetric information and random price fluctuations at finance markets, Proc. Appl. Ind. Math. 12(4), 950–952 (in Russian)] investigated a game [Formula: see text] modeling multistage bidding with asymmetrically informed agents and proved that for this game [Formula: see text] converges to a finite limit [Formula: see text], i.e., the error term is [Formula: see text]. In this paper, we show that for this example [Formula: see text] converges to the limit exponentially fast. For this purpose we apply the optimal strategy [Formula: see text] of insider in the infinite-stage game obtained by Domansky [(2007) Repeated games with asymmetric information and random price fluctuations at finance markets, Int. J. Game Theor. 36(2), 241–257] to the [Formula: see text]-stage game and deduce that it is [Formula: see text]-optimal with [Formula: see text] exponentially small.

A study on fuzzy rough continuous differential games

Our purpose is to propose the solution of two person zero-sum continuous differential games in the fuzzy rough environment. This paper uses fuzzy rough sets to measure the dual and multiple uncertainties with high ambiguity and vagueness in continuous differential games. The combination of fuzzy and rough set in continuous differential games represents a new class defined as fuzzy rough continuous differential games. Two person zero-sum fuzzy rough continuous differential games sufficient and necessary conditions are achieved and numerical example is carried out to support the theoretical claims.

Comparison of QEEG Findings between Adolescents with Attention Deficit Hyperactivity Disorder (ADHD) without Comorbidity and ADHD Comorbid with Internet Gaming Disorder.

Internet gaming disorder (IGD) is often comorbid with attention deficit hyperactivity disorder (ADHD). In this study, we compared the neurobiological differences between ADHD comorbid with IGD (ADHD+IGD group) and ADHD without comorbidity (ADHD-only group) by analyzing quantitative electroencephalogram (QEEG) findings. We recruited 16 male ADHD+IGD, 15 male ADHD-only adolescent patients, and 15 male healthy controls (HC group). Participants were assessed using Young's Internet Addiction Scale and ADHD Rating Scale. Relative power and inter- and intra-hemispheric coherences of brain waves were measured using a digital electroencephalography (EEG) system. Compared to the ADHD-only group, the ADHD+IGD group showed lower relative delta power and greater relative beta power in temporal regions. The relative theta power in frontal regions were higher in ADHD-only group compared to HC group. Inter-hemispheric coherence values for the theta band between F3–F4 and C3–C4 electrodes were higher in ADHD-only group compared to HC group. Intra-hemispheric coherence values for the delta, theta, alpha, and beta bands between P4–O2 electrodes and intra-hemispheric coherence values for the theta band between Fz–Cz and T4–T6 electrodes were higher in ADHD+IGD group compared to ADHD-only group. Adolescents who show greater vulnerability to ADHD seem to continuously play Internet games to unconsciously enhance attentional ability. In turn, relative beta power in attention deficit in ADHD+IGD group may become similar to that in HC group. Repetitive activation of brain reward and working memory systems during continuous gaming may result in an increase in neuronal connectivity within the parieto-occipital and temporal regions for the ADHD+IGD group.

Game among interdependent networks: The impact of rationality on system robustness

Many real-world systems are composed of interdependent networks that rely on one another. Such networks are typically designed and operated by different entities, who aim at maximizing their own payoffs. There exists a game among these entities when designing their own networks. In this paper, we study the game investigating how the rational behaviors of entities impact the system robustness. We first introduce a mathematical model to quantify the interacting payoffs among varying entities. Then we study the Nash equilibrium of the game and compare it with the optimal social welfare. We reveal that the cooperation among different entities can be reached to maximize the social welfare in continuous game only when the average degree of each network is constant. Therefore, the huge gap between Nash equilibrium and optimal social welfare generally exists. The rationality of entities makes the system inherently deficient and even renders it extremely vulnerable in some cases. We analyze our model for two concrete systems with continuous strategy space and discrete strategy space, respectively. Furthermore, we uncover some factors (such as weakening coupled strength of interdependent networks, designing a suitable topology dependence of the system) that help reduce the gap and the system vulnerability.

Evolutionary Stability of Polymorphic Population States in Continuous Games

In games with continuous strategy spaces, if a rest point of the replicator dynamics is asymptotically stable then the rest point must be finitely supported (van Veelen, M., Spreij, P., 2009. Evolution in games with a continuous action space. Econom. Theory 39 (3), 355-376). In this article, we address the converse question that is, we prove that a finitely supported population state is asymptotically stable with respect to the variational norm when it is strongly uninvadable.

A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games.

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful.

On the Characterization of Local Nash Equilibria in Continuous Games

We present a unified framework for characterizing local Nash equilibria in continuous games on either infinite-dimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient first- and second-order conditions ensuring strategies constitute local Nash equilibria. We term points satisfying the sufficient conditions differential Nash equilibria . Further, we provide a sufficient condition (non-degeneracy) guaranteeing differential Nash equilibria are isolated and show that such equilibria are structurally stable. We present tutorial examples to illustrate our results and highlight degeneracies that can arise in continuous games.

Scoring and general match profile of Super Rugby between 2008 and 2013

Rugby research has focused on a range of performance indicators related to game structures and tactical aspects. The purpose of this study was to investigate and compare the effect of law changes on the match profile of Super Rugby between the 2008 and 2013 seasons. For the purpose of this study the researchers made use of mixed-method methodology. A total of 646 Super Rugby matches were recorded and analyzed by means of the Fairplay video analysis software package. Further semi-structured interviews were conducted with expert coaches, specialist coaches, players and referees and referee coaches. Results revealed a significant increase in the number of points scored (p<0.01) and a decrease in the number of tries scored (p<0.01). Results of the study show that the profile of Super Rugby has changed to a more continuous game dynamic with the increase in the number of ball carries (d=1.34), passes (d=0.43), tackle breaks (d=1.59) and line breaks (d=2.40), and has led to an increase in the number of tackles (d=0.63). A decrease in the number of rucks (d=1.73), mauls (d=0.63), scrums (d=0.27) and scrum resets (d=1.36) was found. An increase in penalty kicks (d=2.04) and a decrease in free kicks (d=0.4.53) between 2008 and 2013 were observed. The general match profile of Super Rugby has moved to a game with fewer scrums and kicks and more ball carries and tackles. According to the interviewed experts, good playing surfaces in the Southern Hemisphere allow for an open-game approach by the teams.

Evolutionary stability in continuous nonlinear public goods games.

We investigate a type of public goods games played in groups of individuals who choose how much to contribute towards the production of a common good, at a cost to themselves. In these games, the common good is produced based on the sum of contributions from all group members, then equally distributed among them. In applications, the dependence of the common good on the total contribution is often nonlinear (e.g., exhibiting synergy or diminishing returns). To date, most theoretical and experimental studies have addressed scenarios in which the set of possible contributions is discrete. However, in many real-world situations, contributions are continuous (e.g., individuals volunteering their time). The "n-player snowdrift games" that we analyze involve continuously varying contributions. We establish under what conditions populations of contributing (or "cooperating") individuals can evolve and persist. Previous work on snowdrift games, using adaptive dynamics, has found that what we term an "equally cooperative" strategy is locally convergently and evolutionarily stable. Using static evolutionary game theory, we find conditions under which this strategy is actually globally evolutionarily stable. All these results refer to stability to invasion by a single mutant. We broaden the scope of existing stability results by showing that the equally cooperative strategy is locally stable to potentially large population perturbations, i.e., allowing for the possibility that mutants make up a non-negligible proportion of the population (due, for example, to genetic drift, environmental variability or dispersal).

Communication and Cooperation: A Methodological Study

We study the effect of communication in an experimental game where cooperation is consistent with equilibrium play. We examine two methodological questions which affect many studies of communication in games, particularly those studying the relationship between communication and cooperation in supergames. We show that making it easier for subjects to reach an agreement (by allowing more rounds of communication) does not increase cooperation with a limited message space treatment. Thus, limited message space treatments are not a good substitute for the use of chat. Making the game longer, thereby making the connection between the first period and the continuation game more obvious, also has little impact on cooperation. For both the two- and three-period versions of our game we find substantial amounts of contingent play. This implies that use of a finitely repeated game, which has a number of methodological advantages, maintains the main properties of the underlying supergame.

One Round Voronoi Game on Grids

Recently there has been a great deal of interest in Voronoi Game: Two players insert a certain number of facilities in a determined number of rounds. The Voronoi Diagram of the inserted facilities is calculated and the winner is settled based on the Voronoi Region occupied by either of the players. A special version of the game in which the players insert their facilities in a single round is called ”One Round Voronoi Game”. Most of the previous studies in this area are performed in continuous game regions and facilities are considered as single points in the region with no area. In this paper, a new approach to One Round Voronoi Game is presented. Two players insert their facilities on a rectangular grid in one round. The area of the grid is shared between the players based on the nearest neighbor rule with Manhattan metric. Winning strategies are proposed for the first player in both one and two dimensional grids and the optimality of the strategy is proven in the one-dimensional case. Furthermore, the lower bound of winning margin is presented in both cases.

The Problem with All-or-Nothing Trust Games: What Others Choose Not to Do Matters in Trust-Based Exchange

Many economic interactions are characterized by “all-or-nothing” action spaces that may limit the demonstrability of intended trust. We investigate whether restricting investment opportunities to all-or-nothing options affects the investment rate and propensity to reciprocate. We do this by manipulating the investor’s action space in two versions of the trust game. In the all-or-nothing game the investor can invest either $10 (all) or $0 (nothing), while in the continuous game the investor can invest any amount between $10 and $0. In both games, the trustee receives the tripled investment and then can return any amount to the investor. Results indicate that investments are higher in the all-or-nothing game than in the continuous game. However, higher investments in the all-or-nothing game do not lead to higher returns. To the contrary, conditional on $10 investments, on average trustees return less in the all-or-nothing game. Although the all-or-nothing action space results in greater wealth overall, it also appears to “backfire” for investors who do not benefit from the increased wealth. These results support the proposition that humans perceive intentions not only by evaluating what others do but also by evaluating what others choose not to do.

奥巴马执政以来中美在东南亚地区影响力比较分析/A Comparative Analysis of the Influence of China and the United States in the Southeast Asia Region under the Obama Administration

随着中国的加速崛起以及奥巴马政府“重返亚太”战略的实施，中美与东南亚地区的关系在近年发生了很多变化，在东南亚地区的影响力也随之变化。中美两国在政治、经济、军事、文化等方面都加强了与东南亚地区的关系，对东南亚地区的影响力都有不同程度的增长。比较而言，中国对东南亚的经济影响力更大，而美国对其军事以及安全方面的影响力更大。中国大力推行以“亲、诚、惠、容”为理念的周边外交政策，美国积极推进“亚太再平衡”战略，而东南亚各国则继续选择“在经济上依赖中国、在安全上依靠美国”的大国平衡战略，这导致了中美在东南亚地区影响力的持续博弈。 With China’s rapid rise and the implementation of the Obama Administration’s ”Return to the Asia Pacific” strategy, both China and the United States have significantly changed their relations with Southeast Asia in recent years. Also, the influence of China and the United States in this region has changed too. Both China and the United States have strengthened relations with the Southeast Asia region in terms of political, economic, military, cultural and other aspects, and their influence has also risen in varying degrees. In comparison, China has a greater impact on the economy of Southeast Asia, while the US has more influence on its military and security. China vigorously implements the neighborhood diplomacy featuring amity, sincerity, mutual benefit and inclusiveness. The United States actively promotes the Asia-Pacific rebalancing strategy. The Southeast Asian countries continue to choose the balance of power strategy, relying on China regarding the economy, relying on the United States regarding the security. This has resulted in the continuous game between China and the United States in the Southeast Asian region.

From data to disruption

Organized crime groups and law enforcement agencies are caught in complex system similar to a continuous game of cat-and-mouse, in which the latter frequently remains two or more steps behind. Law enforcement agencies are therefore seeking for more proactive strategies in targeting these criminal network structures more effectively. This starts with a better understanding of the way they operate and adapt over time. A key element to developing this understanding remained largely unexploited: big data and big data analytics. This provides novel insight into how criminal cooperations on a micro- and meso level are embedded in small-world criminal macro-networks and how this fosters its resillience against disruption. This paper discusses the opportunities and the limitations of this data-driven approach and its implications for both law enforcement practice and scientific research.

Mixed and Continuous Strategy Monitor-Forward Game Based Selective Forwarding Solution in WSN

Wireless sensor networks are often deployed in unattended and hostile environments. Due to the resource limitations and multihop communication in WSN, selective forwarding attacks launched by compromised insider nodes are a serious threat. A trust-based scheme for identifying and isolating malicious nodes is proposed and a mixed strategy and a continuous strategy Monitor-Forward game between the sender node and its one-hop neighboring node is constructed to mitigate the selective dropping attacks in WSN. The continuous game will mitigate false positives on packet dropping detection on unreliable wireless communication channel. Simulation results demonstrate that continuous Monitor-Forward game based selective forwarding solution is an efficient approach to identifying the selective forwarding attacks in WSN.

Gamble While You Gamble: Electronic Games in Ontario Charitable Gaming Centres.

Electronic Bingo games have recently appeared in Ontario Charitable Gaming Centres. Here we summarize the characteristics of this novel form of electronic gambling, and give a detailed characterization of one game. We contend that these games have structural characteristics that make them similar to modern Electronic Gaming Machines (EGMs) that feature multiline slots games. These features include a fast and continuous gaming experience, with player adjustable win size and reinforcement rate, a high frequency of losses disguised as wins, and highly salient near misses. Some of these games also have bonus rounds and provide players with a list of recent wins. We conclude that provincial and state gaming authorities should be aware that the placement of Bingo EGMs in existing Bingo facilities may increase problem gambling among an already well-established community of Bingo enthusiasts.

Self-Triggered Best-Response Dynamics for Continuous Games

Motivated by the development of novel and practically implementable coordination algorithms for multi-agent systems, here we investigate the adaptation of classical best-response dynamics by means of self-triggered communications. First, we show that, if the best response dynamics is defined for a continuous-action-space potential game, convergence towards the Nash Equilibria set is guaranteed under continuity on utilities and component-wise pseudo-concavity of the potential function. Then, we modify the best-response dynamics to account for more economic self-triggered communication strategies while ensuring convergence to the equilibrium set. The proposed algorithm is then analyzed in the framework of hybrid systems theory.

Study on Mixed Strategy Nash Equilibrium Based on Rough Set Theory and Particle Swarm Optimization

There is at least one mixed strategy Nash equilibrium in continuous game, but the existing literature does not provide a universal method of solving infinite strategy mixed strategy NASH equilibrium; this is also the issues to be ad- dressed in the paper. This paper creates a infinitely strategy mixed strategy Nash equilibrium's an approximation algo- rithm, using rough set theory and the advantages of particle swarm optimization. And proposes the concept of fuzzy game theory, gives a method converted fuzzy game to a classic game theory base on rough set and Vague set theory; The paper provides a theoretical basis for widespread problem in the applications field of game theory when strategy sets and the benefit function problem are fuzzy. The results of the algorithm example show, this paper created algorithm is feasible and effective. It can solve an infinite strategy mixed strategy Nash equilibrium, and equilibrium problem of fuzzy game model.