Infinite Games Research Articles

There is no known nonlinear Markov perfect equilibrium strategies for the infinite horizon linear quadratic differential game

We discuss published accounts of nonlinear equilibrium strategies in linear quadratic differential games. The main reference: Tsutsui-Mino 1990, is shown to be misleading.

The Infinite Game: Opportunities and Lessons About Possible Futures of Anesthesia Service Delivery from the United Kingdom.

The Infinite Game: Opportunities and Lessons About Possible Futures of Anesthesia Service Delivery from the United Kingdom.

A paradoxical perspective on the time dimension of corporate sustainability: having both finite and infinite mindsets to play the game

Adopting a paradoxical perspective, we propose that companies need to have both finite and infinite mindsets to play the infinite game of corporate sustainability (CS). The current development of the paradoxical approach to CS focuses primarily on tension management, with limited attention directed to the time dimension and insufficient empirical evidence on how tensions between the present and the future should be dealt with. To bridge this gap, we empirically explore the effect of CS practices, driven by both finite and infinite mindsets, on CS performance. Data collected from a large-scale survey of Chinese automotive manufacturers were analyzed using the Entropy Weight Method (EWM) and Ordinary Least Squares (OLS) regressions. Findings suggest that a time-based paradoxical perspective on CS exists in firms, and they have realized short- and long-term benefits from implementing different types of CS practices. Our findings complement the CS literature on tension management and encourage businesses and policymakers to take a paradoxical approach to CS processes and outcomes.

Cardinal inequalities involving the weak Rothberger and cellularity games

We prove several results in the theory of topological cardinal invariants involving the game-theoretic versions of the weak Lindelöf degree and of cellularity. One of them is related to Bell, Ginsburg and Woods’s 1978 question of whether every weakly Lindelöf regular first-countable space has cardinality at most continuum and another one is connected with Arhangel’skii’s 1970 question on the weak Lindelöf degree of the Gδ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_\\delta $$\\end{document} topology on a compact space. We provide a few application of our results, including some bounds on the cardinality of sequential and radial spaces. We finish with a series of counterexamples, which show the sharpness of our results and disprove a few natural conjectures about the impact of infinite games on topological cardinal invariants.

Strategy Complexity of Reachability in Countable Stochastic 2-Player Games

AbstractWe study countably infinite stochastic 2-player games with reachability objectives. Our results provide a complete picture of the memory requirements of $$\varepsilon $$ ε -optimal (resp. optimal) strategies. These results depend on the size of the players’ action sets and on whether one requires strategies that are uniform (i.e., independent of the start state). Our main result is that $$\varepsilon $$ ε -optimal (resp. optimal) Maximizer strategies requires infinite memory if Minimizer is allowed infinite action sets. This lower bound holds even under very strong restrictions. Even in the special case of infinitely branching turn-based reachability games, even if all states allow an almost surely winning Maximizer strategy, strategies with a step counter plus finite private memory are still useless. Regarding uniformity, we show that for Maximizer there need not exist memoryless (i.e., positional) uniformly $$\varepsilon $$ ε -optimal strategies even in the special case of finite action sets or in finitely branching turn-based games. On the other hand, in games with finite action sets, there always exists a uniformly $$\varepsilon $$ ε -optimal Maximizer strategy that uses just one bit of public memory.

In what ways do AI techniques propel decision-making amidst volatility? Annotated bibliography perspectives

This research presents a systematic review and approximation, from 2018 to 2023, of how Artificial Intelligence can support decision-making processes when business managers have to resolve between multiple alternatives for the development of new businesses using Agile Frameworks; and as well, will be addressed from the genesis concepts such as VUCA, Agile Mindset, Infinite Game Theory, Agile Frameworks, Innovation, Artificial Intelligence among others with the aim of identifying research gaps in the decision-making process under changing environments. Most of the analyzed studies are focused on Infinity Games theory to better understand innovation processes linked from early stages to deployment phases of products. Furthermore, this paper analyzes AI techniques for decision-making under volatile circumstances and raises 5 research questions that from a logical and chronological perspective in development are resolved during the research. It is important to highlight that AI-related solutions are typically used to make informed decisions; however, few studies adopt AI to support the decision-making process in unstable environments.

A 5C model of responsible service leadership: learning from living systems to play the infinite game

PurposeThis paper offers a new vision of responsible service leadership for service organizations nested in economic, societal and environmental contexts across time to foster collective flourishing.Design/methodology/approachFollowing the call for novel perspectives that recognize service as a game among (vs between) people in service ecosystems, we build on service leadership theory to integrate insights from infinite (vs finite) games and biomimicry practices to propose a holistic model for responsible service leadership.FindingsWe extend the 3C (competence, character and care) model of service leadership (Shek et al., 2021) adding context and chronos as essential pillars of responsible service leadership in nested ecosystems. We offer new interpretations and applications of the 3Cs through the lens of context and chronos.Research limitations/implicationsThis paper furthers the emerging conversation about unique leadership approaches for service, linking existing service leadership theories with holistic views of service ecosystems and enabling a shift from decontextualized models of leadership to a more inclusive approach.Practical implicationsWe propose that responsible service leadership can inspire new approaches to leadership development within organizations and in business education (e.g. competencies, settings) and a reconsideration of organizational structures (e.g. culture, selection and incentive design).Social implicationsThe proposed 5C model revisits foundational assumptions of responsibility in service leadership, integrating actors across and within service ecosystems, society at large and the environment in the present and future.Originality/valueThis paper offers a conceptual framework – the 5Cs model of responsible service leadership – aimed at reimagining service leadership.

Top-down complementation of automata on finite trees

We present a new complementation construction for nondeterministic automata on finite trees. The traditional complementation involves determinization of the corresponding bottom-up automaton (recall that top-down deterministic automata are less powerful than nondeterministic automata, whereas bottom-up deterministic automata are equally powerful).The construction works directly in a top-down fashion, therefore without determinization. The main advantages of this construction are: (i) in the special case of finite words it boils down to the standard subset construction (which is not the case of the traditional bottom-up complementation construction), and (ii) it illustrates the core argument of the complementation lemma for infinite trees, central in the proof of Rabin's tree theorem, in a simpler setting where issues related to acceptance conditions over infinite words and determinacy of infinite games are not present.

Partially observable discrete-time discounted Markov games with general utility

In this paper, we investigate partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both finite and infinite horizon games and also establish the existence of optimal polices. The main step involves converting the partially observable game into a completely observable game which also keeps track of the total discounted accumulated reward/cost.

Education - finite or infinite game?

Today it is readily accepted that learning is in crisis and, as such, the School is in crisis; However, we believe that never before has so much been learned, which is why we will demonstrate that today the School is in crisis because education is in crisis; as such, following in the footsteps of the ancient Greeks, we will distinguish between the technique and the ethics of education, arguing that today’s School has eliminated ethics from the educational process, retaining only technique (the process of instruction). As a result, children no longer know why they should go to school and education seems purposeless; the solution to this crisis is not to perfect the education process but to recover the ethical-value dimension of education. To demonstrate this, we use the finite game/infinite game conceptual binomial developed by John Carse in Infinite and finite games.

Vertical Collusion to Exclude Product Improvement*

A manufacturer of an established product repeatedly interacts with a retailer that can sell an inferior new product thereby improving it. The manufacturer's exclusionary strategy consists of a permanently below‐cost wholesale price and “vertical collusion” with the retailer to exclude via a future reward of a reduced fixed fee. The latter tool is available only in an infinite game. Although contracts include fixed fees, the retailer sells the new product more than what maximizes industry profits. Exclusive dealing or a vertical merger between the manufacturer of the established product and the retailer replicate the vertically integrated outcome and increase prices.

Proximal versus distal temporal orientation in an infinite game: lessons from the 1892 Homestead Massacre

PurposeWorking conditions, pay rates and the rights of workers to collectively negotiate have become important points of discussions in recent years, with support for unions and union applications rising to levels long unseen in America. In many instances, though, companies have responded aggressively. This is not the first time such a dynamic has played out in American business. This study aims to take a fresh look at one of America’s most prominent historical disputes between labor and ownership – the Homestead Massacre of 1892 – to glean lessons from that conflict that remain relevant to today’s business environment.Design/methodology/approachThis study adopts game theory and the principles of repeated interaction to assess how differing discount factors led to differences in time orientations between the workers and the Carnegie company. These differing time orientations affected both the strategy each side deployed in the negotiations and the payoffs received by the parties. Letters, contemporary news reports and histories of the events leading up to and immediately following the 1892 Homestead Massacre are qualitatively analyzed with a genealogical pragmatic approach.FindingsDifferences in temporal orientation between management and workers exacerbated the conflict, with the workers adopting a more cooperative stance and distal time orientation, while the Carnegie company negotiated with a proximal time orientation and played to “win” a game that, in fact, could not be fully won or lost given its infinitely repeating nature. The result was a short-term victory for the Carnegie company but with long-term negative consequences that highlight the suboptimal outcome the company achieved by playing a proximal strategy in an infinite game.Originality/valueAlthough the incident at Homestead is a well-studied labor dispute, many of the themes that preceded the incident have resurfaced in the modern work context. This work, by adopting game theory as an analytical framework, provides new insights into management mistakes that led to the labor conflict and lessons for what present-day managers can do to avoid exacerbating labor strife.

Expected Policy Gradient for Network Aggregative Markov Games in Continuous Space.

In this article, we investigate the Nash-seeking problem of a set of agents, playing an infinite network aggregative Markov game. In particular, we focus on a noncooperative framework where each agent selfishly aims at maximizing its long-term average reward without having explicit information on the model of the environment dynamics and its own reward function. The main contribution of this article is to develop a continuous multiagent reinforcement learning (MARL) algorithm for the Nash-seeking problem in infinite dynamic games with convergence guarantee. To this end, we propose an actor-critic MARL algorithm based on expected policy gradient (EPG) with two general function approximators to estimate the value function and the Nash policy of the agents. We consider continuous state and action spaces and adopt a newly proposed EPG to alleviate the variance of the gradient approximation. Based on such formulation and under some conventional assumptions (e.g., using linear function approximators), we prove that the policies of the agents converge to the unique Nash equilibrium (NE) of the game. Furthermore, an estimation error analysis is conducted to investigate the effects of the error arising from function approximation. As a case study, the framework is applied on a cloud radio access network (C-RAN) by modeling the remote radio heads (RRHs) as the agents and the congestion of baseband units (BBUs) as the dynamics of the environment.

The $$\kappa $$-core and the $$\kappa $$-balancedness of TU games

AbstractWe consider transferable utility cooperative games with infinitely many players. In particular, we generalize the notions of core and balancedness, and also the Bondareva–Shapley Theorem for infinite TU games with and without restricted cooperation, to the cases where the core consists of $$\kappa $$ κ -additive set functions. Our generalized Bondareva–Shapley Theorem extends previous results by Bondareva (Problemy Kibernetiki 10:119–139, 1963), Shapley (Naval Res Logist Q 14:453–460, 1967), Schmeidler (On balanced games with infinitely many players, The Hebrew University, Jerusalem, 1967), Faigle (Zeitschrift für Oper Res 33(6):405–422, 1989), Kannai (J Math Anal Appl 27:227–240, 1969; The core and balancedness, handbook of game theory with economic applications, North-Holland, 1992), Pintér (Linear Algebra Appl 434(3):688–693, 2011) and Bartl and Pintér (Oper Res Lett 51(2):153–158, 2023).

The Infinite Game: One Possible Future of Anesthesia in the United States.

The Infinite Game: One Possible Future of Anesthesia in the United States.

Subgame-perfect Equilibria in Mean-payoff Games (journal version)

In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the notion of negotiation function. We establish that the plays that are supported by SPEs are exactly those that are consistent with a fixed point of the negotiation function. Finally, we use that characterization to prove that the SPE threshold problem, who status was left open in the literature, is decidable.

Synchronization in a Kuramoto mean field game

The classical Kuramoto model is studied in the setting of an infinite horizon mean field game. The system is shown to exhibit both synchronization and phase transition. Incoherence below a critical value of the interaction parameter is demonstrated by the stability of the uniform distribution. Above this value, the game bifurcates and develops self-organizing time homogeneous Nash equilibria. As interactions get stronger, these stationary solutions become fully synchronized. Results are proved by an amalgam of techniques from nonlinear partial differential equations, viscosity solutions, stochastic optimal control and stochastic processes.

Switching global correlations on and off in a many-body quantum state by tuning local entanglement.

A quantum many-body state built on a classical 1D Ising model with locally entangled qubits is considered. This setup can model an infinite player quantum Prisoner's dilemma game with each site representing two entangled players (or qubits). The local entanglement γ between two qubits placed on a site in the 1D Ising model and classical coupling between adjacent sites of the Ising model have an apposite influence on qubits. It points to a counter-intuitive situation wherein local entanglement at a site can exactly cancel global correlations, signaling an artificial quantum many-body state wherein, by locally tuning the entanglement at a particular site, one can transition from a strongly correlated quantum state to an uncorrelated quantum state and then to a correlated classical state. In other words, we can simulate a state similar to a type II superconducting state via local tuning of entanglement in a 1D Ising chain with entangled qubits.

Indonesian Higher Education Institution’s Strategy toward Disruption with Implementation of Infinite Games Mindset

Indonesian Higher Education Institution’s Strategy toward Disruption with Implementation of Infinite Games Mindset

Proximal versus Distal Temporal Orientation in an Infinite Game: Lessons from the Homestead Massacre

Proximal versus Distal Temporal Orientation in an Infinite Game: Lessons from the Homestead Massacre