# gst: natural invariant measures for chaotic game dynamics; finding order in chaos.

<< ️(AA) study the long-term behavior of the Multiplicative Weights Update (MWU) algorithm in game settings where learning dynamics frequently fail to converge to Nash equilibria and instead exhibit Li-Yorke chaos. While such chaos precludes the prediction of specific long-term strategy profiles, it does not imply a lack of statistical structure. >>

<< ️(AA) demonstrate that natural invariant measures — a fundamental concept from ergodic theory — provide the rigorous framework necessary to find order within this chaos. Focusing on a two-strategy congestion game, (They) prove that these measures allow for a comprehensive statistical characterization of the dynamics. Crucially, (They) show that this framework extends beyond simple strategy frequencies to general observables, enabling the precise calculation of long-term time averages for broad classes of economic metrics — including payoffs, social cost, and regret — despite chaos. >>

<< ️(They) results reveal that this simple learning algorithm captures the full spectrum of behaviors found in one-dimensional dynamical systems, from unique or multiple absolutely continuous invariant measures to complex periodic attractors as well as coexisting chaotic and stable (periodic) behaviors. By bridging game theory and dynamical systems, (AA) show that statistical predictability is attainable even in the absence of pointwise convergence. >>

<< ️The intersection of game theory, dynamical systems, computer science, and statistics is rich with open questions, particularly when considering learning dynamics in games. >>

Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski, et al. Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos. arXiv: 2607.21805v1 [math.DS]. Jul 23, 2026.

https://arxiv.org/abs/2607.21805

Also: game, chaos, order, disorder,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, game, chaos, Multiplicative Weights Update (MWU) algorithm, statistical structure, statistical predictability, two-strategy congestion game, complex periodic attractors, coexisting chaotic and stable (periodic) behaviors.

# s-game: #POTUS race turned into a game theory experiment ...

<< Zollman [Kevin  Zollman, Carnegie  Mellon University] notes being among the first to endorse a candidate who is best positioned  to  win  has its  advantages.  “You  get more credibility,”  he  said.  “I  want to  endorse  early  so  I can say, ‘I was there first’  —  the political  version  of  being  a hipster.” >>

<< That’s  what game theorists call  “costly  signaling,”  a  concession  an  individual makes to indicate greater  strength. Academics  have  theorized  that  the  sharing  of food  in  hunter-gatherer  societies  might  not  be  primarily  altruistic,  but  rather  a chance for the best hunters to show off their skills,  and  thereby  move up in the reproductive  pecking  order. >>

<< But  that  was  before  the  2016 race turned into a game theory experiment, where true feelings are set aside for the purpose of a single  mathematical  result. >>

Andrew McGill. The Anti-Trump Endorsement Game. The mathematical strategy behind endorsing Ted Cruz, as explained by game theory. The  Atlantic. March 25, 2016

http://www.theatlantic.com/politics/archive/2016/03/trump-cruz-kasich-endorsement/475230/ 

<< (..) another  turn  of  the  cards  in  a  game  that  refuses  to  conform  to  old  rules.  The winner  will  be  the  candidate  who  figures  out  the  new  ones. >>

Andrew  McGill. The Game  Theory  Principles  Behind  a  Political Endorsement  Against  Trump. The  Atlantic. March  27,  2016.

http://m.govexec.com/oversight/on-politics/2016/03/game-theory-principles-behind-political-endorsement-against-trump/126971/

# life: epistemic horizon minority games: when abundance reduces strategic value.

<< ️In ordinary language, abundance suggests value. In strategic systems this intuition often fails. >> 

<< ️Strategic value can fall when an option becomes visible. A route, signal, bet, or opportunity may be attractive because few agents see it; public attention can erase the advantage it reveals. >>

<< ️(AA) formalize this mechanism as an epistemic-horizon minority game (EHMG), where agents have bounded observation horizons, action-specific awareness, desire-biased utilities, and payoffs that decline with crowding, and where the object is not a fixed congestion game with omitted actions but an awareness-transition game on a finite lattice. (They) prove fixed-awareness potential-game reduction, finite monotone awareness convergence, logit mean-field uniqueness under an explicit norm condition, non-reducibility from static count-based congestion games, and sensitivity bounds for nonlinear revelation. >>

<< ️(AA) separate the target price of information from aggregate welfare loss, showing that they can coincide, diverge, or recommend opposite disclosure policies, while modeling private revelation, public common revelation, and correlated group disclosure as distinct signal structures with different equilibrium effects. Experiments regenerate awareness sweeps, public visibility shocks, horizon-desire grids, information-constrained Braess examples, disclosure optimization, minimum harmful revelation, and counterfactual baselines isolating the epistemic mechanism from ordinary full-awareness congestion. >>

<< ️Strategic trace encodings are evaluated as a controlled regime-recognition benchmark using raw trajectories, Fourier summaries, recurrence and Gramian images, image bundles, local-filter features, leakage probes, phase-scrambled controls, resolution and recurrence-threshold sweeps, spectral carriers, and IAAFT-matched null parameter-shift controls to test whether trace encodings recover strategic structure under robust nulls. >>

Faruk Alpay, Levent Sarioglu. Epistemic Horizon Minority Games: When Abundance Reduces Strategic Value. arXiv: 2607.02765v1 [cs.GT]. Jul 2, 2026.

https://arxiv.org/abs/2607.02765

Also: game, in https://www.inkgmr.net/kwrds.html 

Keywords: game, life, strategic values, epistemic-horizon minority game (EHMG), awareness-transition game, awareness sweeps, disclosure optimization, aggregate welfare loss, minimum harmful revelation, leakage probes, full-awareness congestion, recurrence-threshold sweeps, robust nulls. 

# game: inject irrationality into a game scenario; when a player will be their own worst enemy

<< in game theory, a game is defined as any type of scenario where there's an interaction between different decision-makers, or players, each of whom has well-defined preferences. >>

<< previous analyses assume the decision-makers always do what is best for them-they are fully rational-which is not always realistic. >>

<< So SFI Professor David Wolpert and economist Justin Grana, a former SFI postdoctoral scholar, wanted to inject some humanity into the players. They analyzed games with players who were subject to error, or "boundedly rational." >>

<< Our analysis shows that in many of these situations, a player will be their own worst enemy; >> David Wolpert.

Jenna Marshall. How much would you pay to change a game before playing it? Santa Fe Institute. Aug13, 2019.    https://m.phys.org/news/2019-08-game.html  

David Wolpert, Justin Grana. How Much Would You Pay to Change a Game before Playing It? Entropy 2019, 21, 686. doi: 10.3390/ e21070686. July 13, 2019.   https://www.mdpi.com/1099-4300/21/7/686  

# game: in a iterated prisoner's dilemma scenario forgiveness turns out to be an adaptation

<< Prisoner’s dilemma is used to represent a range of real life phenomena such as economics, commerce, nature and wildlife. >>

<< Researchers working on iterated prisoner's dilemma (IPD) with limited memory inspected the outcome of different forgetting strategies in homogeneous environment, within which all agents adopt the same forgetting strategy at a time. In this work, with the intention to represent real life more realistically, (AA) improve existing forgetting strategies, offer new ones, and conduct experiments in heterogeneous environment that contains mixed agents and compare the results with previous research as well as homogeneous environment >>

<< in a more realistic environment consisting of all types of agents, in terms of both cooperation probabilities and forgetting strategies, agents who forget defectors consistently outperform other forgetting strategies for all memory ratio values. Moreover, the best performing defectors are also the ones that forget other defectors. In other words, agents who “forgive” defectors are the best performers. Hence, forgiveness is an adaptation. >>

FMC : Forget most cooperator first 

FMP : Forget most played first 

FMU : Forget most unpredictable first 

FR :  Forget randomly 

FLP : Forget least played first 

FMD : Forget most defector first 

Meliksah Turker, Haluk O. Bingol. Forgiveness is an Adaptation in Iterated Prisoner's Dilemma with Memory. arXiv:2112.07894v1 [cs.GT]. Dec 15, 2021

https://arxiv.org/abs/2112.07894

Also

keyword 'game' | 'tit-for-tat' in FonT

https://flashontrack.blogspot.com/search?q=game

https://flashontrack.blogspot.com/search?q=tit-for-tat

keyword 'game' | 'tit-for-tat' in Notes

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=game

https://inkpi.blogspot.com/search?q=tit-for-tat

Keywords: game, iterated prisoner's dilemma, forgiveness, adaptation

# life: to protect freedoms, not just funding.

<< At Harvard University in Cambridge, Massachusetts, and Columbia University in New York City, cuts to previously granted federal research funds have been accompanied by demands from the government. If enacted, the changes to departmental oversight, disciplinary procedures, campus police and governance structures would allow the government to dictate hiring, student admissions and disciplinary decisions. >>

<< So far, the US science community has been outspoken about the threats that funding cuts pose to health, innovation and the economy. Yet, few researchers have decried the devastation wreaked on science by attacks on civil liberties and the rule of law. >>

Andrew M. Leifer, Andrea J. Liu, Sidney R. Nagel. US researchers must stand up to protect freedoms, not just funding. Nature 641, 592-593. May 13, 2025.

https://www.nature.com/articles/d41586-025-01466-5

Also: people who turn career into a game playing ... FonT. May 31, 2017.

https://flashontrack.blogspot.com/2017/05/s-game-people-who-turn-career-into-game.html

Also: minimal risk, in FonT 

https://flashontrack.blogspot.com/search?q=minimal+risk

Also: acad, in Font https://flashontrack.blogspot.com/search?q=acad.  acad, in Notes (quasi-stochastic poetry) https://inkpi.blogspot.com/search?q=acad

Also:  dance, game, transition, sars* covid* (aka 1or2achoos), forms of power, Mr. Donald, are you ready, in https://www.inkgmr.net/kwrds.html 

Also: nefst (e.g. not embedded, freestyle thinker) 

https://quod.lib.umich.edu/m/middle-english-dictionary/dictionary/MED20173/track

Keywords: life, acad, game, dance, transitions, nefst, 1or2achoos, minimal risk, turn career, forms of power, Mr. Donald, are you ready.

# s-game: people who turn career into a game playing ...

AA << speak to a researcher who's fascinated by what happens to people who turn game playing into a career >>

Annabel Bligh, Emily Lindsay Brown, et al. Anthill 13: All the world’s a game. May 17, 2017 10.04am BST

http://theconversation.com/anthill-13-all-the-worlds-a-game-77763

https://theconversation.com/uk/topics/gaming-1806

FonT

1618 - etica d'inversione. May 26, 2005 12:16 AM

http://inkpi.blogspot.it/2005/05/1618-etica-dinversione.html

# game: apropos of Parrondo's game, how a flexible parasite can outsmart its hosts for evolutionary dominance.

<< Antagonistic coevolution between hosts and parasites substantially impacts community structure, with parasites displaying fluctuating selection or arms race dynamics during coevolution. The traditional matching alleles (MA) and gene-for-gene (GFG) models have been used to describe the dynamics and interaction of host-parasite coevolution, with these models assuming that parasites adopt a single strategy when competing with other parasites. >>

AA << present a nonlinear dynamic population model that challenges this assumption, showing how a parasite that is disadvantaged under either the MA or the GFG model can win the competition by switching between the two losing strategies based on an external environmental cue, internal processes, or stochastic decision-making. >>

<< This counterintuitive outcome is analogous to Parrondo's paradox, a game-theoretic concept that shows how alternating between two losing strategies can result in a winning outcome. >>

Tao Wen, Eugene V. Koonin, Kang Hao Cheong. How flexible parasites can outsmart their hosts for evolutionary dominance. Phys. Rev. Research 6, 023104. Apr 30, 2024.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.023104 

Also: game, Parrondo, evolution, in https://www.inkgmr.net/kwrds.html 

Keywords: game, Parrondo, evolution

FonT: from my point of view, if well modulated, the two paired strategies "Stochastic Tit-For-Tat" and "Parrondo" are deadly, regardless of the aims of the objectives (cooperative purposes, parasitism, etc)

# s-game: equilibrium, a chimeric target

<< In 1950, John Nash — the mathematician later featured in the book and film “A Beautiful Mind” — wrote a two-page paper that transformed the theory of economics. His crucial, yet utterly simple, idea was that any competitive game has a notion of equilibrium: a collection of strategies, one for each player, such that no player can win more by unilaterally switching to a different strategy >>

<< Nash’s equilibrium concept, which earned him a Nobel Prize in economics in 1994, offers a unified framework for understanding strategic behavior not only in economics but also in psychology, evolutionary biology and a host of other fields. Its influence on economic theory “is comparable to that of the discovery of the DNA double helix in the biological sciences,” wrote Roger Myerson of the University of Chicago, another economics Nobelist >>

In a paper posted online last September AA << proved that no method of adapting strategies in response to previous games — no matter how commonsensical, creative or clever — will converge efficiently to even an approximate Nash equilibrium for every possible game. It’s “a very sweeping negative result,” Roughgarden (Tim Roughgarden) said >>

Erica Klarreich. In Game Theory, No Clear Path to Equilibrium. July 18, 2017.

https://www.quantamagazine.org/in-game-theory-no-clear-path-to-equilibrium-20170718/

Yakov Babichenko, Aviad Rubinstein. Communication complexity of approximate Nash equilibria. arXiv:1608.06580 Sep. 13,  2016

https://arxiv.org/abs/1608.06580

# s-game: a "Colonel Blotto" approach inside a POTUS election: however, the behavior of individuals is not yet well understood ...

<< A team of computer scientists (..) is the first to solve a game theory scenario that has vexed researchers for nearly a century. The game, known as "Colonel Blotto," has been used to analyze the potential outcomes of elections and other similar two-party conflicts since its invention in 1921.>>

<< This solution enabled the team to develop a generalized algorithm, which can now be applied to specific scenarios, such as the 2016 presidential election. >>

<< From presidential elections to marketing decisions, competition for attention and loyalty is a part of daily life. However, the behavior of individuals in response to such competitions is not yet well understood >>

http://phys.org/news/2016-02-team-well-known-game-theory-scenario.html

AmirMahdi Ahmadinejad, Sina Dehghani, et al. From Duels to Battlefields: Computing Equilibria of Blotto and Other Game. Association for the Advancement of Artificial Intelligence (AAAI) Conference in Phoenix, Arizona, February 15, 2016.

http://www.aaai.org/Conferences/conferences.php

more:

https://en.m.wikipedia.org/wiki/Blotto_games

# game: inside an irregular 'rock-paper-scissors' game; 'uneveness nomads' will survive, probably ...

AA << study a class of the stochastic May-Leonard models, with three species dominating each other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. (They) introduce an unevenness in the system, by considering that one of the species is weaker because of a lower selection probability. >>

To << investigate the coexistence probability (..) the surviving species depends on the level of unevenness of the model and the mobility of individuals. >>

Menezes J., Moura B., Pereira TA. Uneven rock-paper-scissors models: Patterns and coexistence. EPL -  Europhysics Letters, Volume 126, Number 1. May 22, 2019.

https://iopscience.iop.org/article/10.1209/0295-5075/126/18003/meta   

Lisa Zyga. The rock-paper-scissors game and coexistence. Phys.org.
Jul 4, 2019

https://m.phys.org/news/2019-07-rock-paper-scissors-game-coexistence.html   

# s-game: fair games if a child thinks life is unfair

Paul Raeburn, co-author of “The Game Theorist's Guide to Parenting” <<suggests applying classic game theory strategies to help children make “fair” decisions and stop the squabbling>>

KJ Dell'Antonia. When a Child Thinks Life Is Unfair, Use Game Theory. July 5, 2016

http://mobile.nytimes.com/blogs/well/2016/07/05/when-a-child-thinks-life-is-unfair-use-game-theory/

# game: pulsating as a Toffoli gate: Parrondo's paradox with a three-state coin (heads, tails, and a side)

<< Parrondo's paradox - an apparent paradox in which two losing strategies combine to make a winning strategy - can emerge as a coin game with a single coin in the quantum realm, but only when the coin has three states (heads, tails, and a side) rather than the conventional two. >>

<< In the new study, [AA] have demonstrated a Parrondo's game using a three-state coin, which they represent with a qutrit, a quantum system with three states. >>

Lisa Zyga. Parrondo's paradox with a three-sided coin. Phys.org. July 11, 2018.

https://m.phys.org/news/2018-07-parrondo-paradox-three-sided-coin.html

Jishnu Rajendran, Colin Benjamin. Playing a true Parrondo's game with a three-state coin on a quantum walk. EPL. 2018; 122(4). June 28.

http://iopscience.iop.org/article/10.1209/0295-5075/122/40004/meta

https://arxiv.org/abs/1710.04033

Also

"Toffoli gate"

# qubit: three-qubit operation with the Toffoli gate for scalable semiconductor quantum processors. Mar 4, 2018.

https://flashontrack.blogspot.com/2018/03/qubit-three-qubit-operation-with.html

FonT

quando lessi per la prima volta in bibliografia circa il "Parrondo Game"  mi venne in mente una strategia che avevo immaginato e piu' volte usato a suo tempo - da meta'  anni '70 a tutti gli anni '80 (e oltre) - composta da una sorta di "tit-for-tat stocastico" cioe' una strategia di gioco di  "cooperazione/ defezione" con decisioni di scelta pilotate da "lancio di moneta" all'interno di due (e poi anche tre) scenari riconducibili al tipo Parrondo ... in pratica la generazione di scenari senz'altro di  "frontiera", evolutivi,  immediatamente generabili all'interno di situazioni (se-si-puo-dire ... or, namely, "sire-die-soup") del tipo "standard", supposte "lineari".  Anzicheforse.

1668 - ramificata tinnula (di carmina fluitantia). Jun 9, 2005.

https://inkpi.blogspot.com/2005/06/1668-ramificata-tinnula-di-carmina.html

"charlie"

https://inkpi.blogspot.com/search?q=charlie

# game: mutual cooperation without non-cooperative actions

AA << have developed a model that consists of all possible strategies using a one-period memory of past actions. This model enables us to analyze a "melting pot" of strategies, wherein several strategies interact and compete with each other. (AA) results revealed that one strategy, in which one escapes if a partner defects or cooperates if a partner becomes a loner, dominates and maintains cooperation in an alternating prisoner's dilemma game. >>

H. Yamamoto, I. Okada, et al.
Effect of voluntary participation on an alternating and a simultaneous prisoner's dilemma.  Phys. Rev. E 100, 032304 Sep 11,  2019.    https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.032304   

The Prisoner's Dilemma: Exploring a strategy that leads to mutual cooperation without non-cooperative actions. Rissho University. Sep 23, 2019.   https://m.phys.org/news/2019-09-prisoner-dilemma-exploring-strategy-mutual.html   

Also

keyword "game" in "FonT"   https://flashontrack.blogspot.com/search?q=game

# game: aperiodic Parrondo (behavior based on the binary Fibonacci, Thue–Morse and Rudin–Shapiro sequences); persistence and heterogeneity effects.

AA << study the effectiveness of employing archetypal aperiodic sequencing -- namely Fibonacci, Thue-Morse, and Rudin-Saphiro -- on the Parrondian effect. From a capital gain perspective, (their) results show that these series do yield a Parrondo's Paradox with the Thue-Morse based strategy outperforming not only the other two aperiodic strategies but benchmark Parrondian games with random and periodical (AABBAABB…) switching as well. The least performing of the three aperiodic strategies is the Rudin-Shapiro. >>

AA << analyze the cross-correlation between the capital generated by the switching protocols and that of the isolated losing games. This analysis reveals that a pronounced anti-correlation (below -0.95) with both isolated games is typically required to achieve a robust manifestation of Parrondo's effect. >>

About << the influence of the sequencing on the capital using the lacunarity and persistence measures (AA) observe that the switching protocols tend to become less performing in terms of the capital as one increases the persistence and thus approaches the features of an isolated losing game. >>

Respect to << lacunarity, a property related to heterogeneity, (AA) notice that for small persistence the performance increases with the lacunarity with a maximum (..). In respect of this, (AA) work shows that  the optimisation of a switching protocol is strongly dependent on a fine tune between persistence and heterogeneity. >>

Marcelo A. Pires, Erveton P. Pinto, et al. Parrondo's effects with aperiodic protocols. arXiv: 2410.02987v1 [physics.soc-ph]. Oct 3, 2024.

https://arxiv.org/abs/2410.02987

Also: Parrondo, tit-for-tat, game, behav, network, in https://www.inkgmr.net/kwrds.html 

Keywords: Parrondo, tit-for-tat, game, behavior, behaviour, network

# game: apropos of Parrondo's paradox, winning with losses driven by reputation and reciprocity

AA << investigate two such social behaviors, reputation and reciprocity, and their role in explaining Darwin’s survival of the fittest, examining how these fundamental principles govern individual interactions and shape broader social dynamics. >>

<< Current theories hint at two main facets of social interaction, reputation and reciprocity, as potential drivers behind this cooperative evolution. Reputation revolves around building and sustaining trust, social worth, and overall community standing. Conversely, reciprocity governs the mutual exchange of actions or benefits, influencing our choices. >>

<< One intriguing concept explored in this domain is Parrondo’s paradox: combining or switching between two losing strategies might surprisingly achieve a winning outcome. The role of Parrondo’s paradox in complex systems has sparked key research into chaotic many-body, quantum, and algorithmic network applications, where combining elements yields opposing beneficial results. Similarly, social physicists aim to uncover hidden mechanisms that govern societal phenomena by integrating the paradox’s counterintuitive principles. >>️

<< The game-theoretic Parrondo’s paradox emerges through multiple iterations of these interactions (..) A naive observation might conclude that in either scheme the chance of individuals losing to the environment is higher than gaining from the environment. For the reputation scheme, one is rewarded with a singular capital from the environment but is punished with two. Similarly, the reciprocity scheme only allows for the redistribution of capital or loss of capital. In reality, diverse schemes can be adopted by different individuals. Thus, (AA) suggest two forms of switching: (1) stochastic switching, where the individual randomly selects one of two schemes to employ with equal probability, and (2) rule-based switching, where the individual only selects the reputation scheme if it passes the reputation threshold ρ; otherwise, it employs the reciprocity scheme. >>

AA << also performed simulations on other network topologies (..) Parrondo’s paradox is strongly observed in small-world networks, weakly in the Erdős-Rényi network, and absent in scale-free networks. >>

To conclude, some of these observations << underscore the profound capability of rule-based switching mechanisms inherent in Parrondo’s paradox to emulate and forecast key aspects of real-world social phenomena. Such insights are invaluable for developing sophisticated models and strategies in various fields, ranging from social sciences to policy making, where accurate predictions of social behavior and dynamics are crucial. >>

Joel Weijia Lai, Kang Hao Cheong. Winning with Losses: The Surprising Success of Negative Strategies in Social Interaction Behavior. Phys. Rev. Lett. 133, 167401. Oct 16, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.167401

Also: Parrondo, tit-for-tat, game, behav, network, in https://www.inkgmr.net/kwrds.html 

Keywords: Parrondo, tit-for-tat, game, behavior, behaviour, network

# game: flocking by turning away.

<< Flocking, as paradigmatically exemplified by birds, is the coherent collective motion of active agents. As originally conceived, flocking emerges through alignment interactions between the agents. >>️

AA << report that flocking can also emerge through interactions that turn agents away from each other. >>

<< Whereas repulsion often leads to motility-induced phase separation of active particles, here it combines with turn-away torques to produce flocking. Therefore, (AA) findings bridge the classes of aligning and nonaligning active matter. (Their) results could help to reconcile the observations that cells can flock despite turning away from each other via contact inhibition of locomotion.  >>️

AA << work shows that flocking is a very robust phenomenon that arises even when the orientational interactions would seem to prevent it. >>️

️

Suchismita Das, Matteo Ciarchi, Ziqi Zhou, Jing Yan, Jie Zhang, Ricard Alert. Flocking by Turning Away. Phys. Rev. X 14, 031008. Jul 12, 2024.

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.14.031008

Also: Janus, in FonT 

https://flashontrack.blogspot.com/search?q=janus 

Also: game, flock, in https://www.inkgmr.net/kwrds.html 

Keywords: game, flock, Janus

FonT: an approach of this type could hypothetically generate intriguing, bizarre, unexpected game scenarios in various other contexts ...

# life: chameleon machines

<< Large language model-based (LLM-based) agents have become common in settings that include non-cooperative parties. In such settings, agents' decision-making needs to conceal information from their adversaries, reveal information to their cooperators, and infer information to identify the other agents' characteristics. To investigate whether LLMs have these information control and decision-making capabilities, (AA) make LLM agents play the language-based hidden-identity game, The Chameleon. >>️

<< Based on the empirical results and theoretical analysis of different strategies, (AA) deduce that LLM-based non-chameleon agents reveal excessive information to agents of unknown identities. (Their) results point to a weakness of contemporary LLMs, including GPT-4, GPT-4o, Gemini 1.5, and Claude 3.5 Sonnet, in strategic interactions. >>

️

Mustafa O. Karabag, Ufuk Topcu. Do LLMs Strategically Reveal, Conceal, and Infer Information? A Theoretical and Empirical Analysis in The Chameleon Game. arXiv: 2501.19398v1 [cs.AI]. Jan 31, 2025.

https://arxiv.org/abs/2501.19398

Also: games, ai (artificial intell), nfulaw, in https://www.inkgmr.net/kwrds.html 

Keywords: life, games, chameleon game, ai, artificial intelligence, LLMs, privacy, nfulaw

# game: hypothesis of a geometric design of chaotic attractors, on demand

AA << propose a method using reservoir computing to generate chaos with a desired shape by providing a periodic orbit as a template, called a skeleton. (They) exploit a bifurcation of the reservoir to intentionally induce unsuccessful training of the skeleton, revealing inherent chaos. The emergence of this untrained attractor, resulting from the interaction between the skeleton and the reservoir's intrinsic dynamics, offers a novel semi-supervised framework for designing chaos. >>️

Tempei Kabayama, Yasuo Kuniyoshi, et al. Designing Chaotic Attractors: A Semi-supervised Approach. arXiv: 2407.09545v1 [cs.NE]. Jun 27, 2024.

https://arxiv.org/abs/2407.09545

Also: game, chaos in https://www.inkgmr.net/kwrds.html 

Keywords: game, chaos, chaotic attractors

# rmx-s-behav: a bizarre paddle game (about safety waves ...)

<< Males of a newly discovered species of jumping spider [Jotus remus] spend hours waving special paddle-shaped legs at prospective mates, in an effort to copulate without being attacked – or even eaten.

Mating can potentially cost you your life if you are a male spider. To avoid becoming lunch, Jotus remus plays a game first to tire out hungry females >>

https://www.newscientist.com/article/dn28756-male-spiders-lure-aggressive-females-with-peek-a-boo-paddle-game/

Jürgen  C.  Otto, David  E.  Hill. Males  of  a  new  species  of  Jotus  from  Australia  wave  a  paddle-shaped lure  to  solicit  nearby  females  (Araneae:  Salticidae:  Euophryini). PECKHAMIA 133.1, 7 January 2016,  1―39 urn:lsid:zoobank.org:pub:12A6DBBE-11EC-4DEB-9387-83F1AD727E6F    (registered  6  JAN  2016) 1 ISSN  2161―8526 (print) ISSN  1944―8120 (online)

http://peckhamia.com/peckhamia/PECKHAMIA_133.1.pdf