Truels and strategies for survival

Dorraki, Mohsen; Allison, Andrew; Abbott, Derek

doi:10.1038/s41598-019-45253-5

Cited by 8 publications

(3 citation statements)

References 20 publications

(18 reference statements)

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“…[15][16][17][18], where a Markov chain formulation of several truel variants is presented; and Refs. [19][20][21], in which truels among N players are studied, with each player being represented by a node in a scale-free network. 1 Several applications of the duel and, more frequently, of the truel have been proposed in the above literature.…”

Section: Introductionmentioning

confidence: 99%

On the Nash Equilibria of a Duel with Terminal Payoffs

Kehagias

2023

Games

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We formulate and study a two-player duel game as a terminal payoffs stochastic game. Players P1,P2 are standing in place and, in every turn, each may shoot at the other (in other words, abstention is allowed). If Pn shoots Pm (m≠n), either they hit and kill them (with probability pn) or they miss and Pm is unaffected (with probability 1−pn). The process continues until at least one player dies; if no player ever dies, the game lasts an infinite number of turns. Each player receives a positive payoff upon killing their opponent and a negative payoff upon being killed. We show that the unique stationary equilibrium is for both players to always shoot at each other. In addition, we show that the game also possesses “cooperative” (i.e., non-shooting) non-stationary equilibria. We also discuss a certain similarity that the duel has to the iterated Prisoner’s Dilemma.

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Section: Introductionmentioning

confidence: 99%

On the Nash Equilibria of a Duel with Terminal Payoffs

Kehagias

2023

Games

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“…This idea is further studied in [13,14,15,25]. Recent papers on the truel include [1,2,3,5,6,7,8,9,22,23,24]. 1 While the above papers focus on various forms of the static truel, we believe that the static duel is interesting in its own right and has not received the attention it deserves.…”

Section: Introductionmentioning

confidence: 99%

A note on the Nash equilibria of some multi-player reachability/safety games

Kehagias¹

2022

JDG

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<p style='text-indent:20px;'>In this short note we study a class of multi-player, turn-based games with deterministic state transitions and reachability / safety objectives (this class contains as special cases "classic" two-player reachability and safety games as well as multi-player and ""stay–in-a-set" and "reach-a-set" games). Quantitative and qualitative versions of the objectives are presented and for both cases we prove the existence of a deterministic and memoryless Nash equilibrium; the proof is short and simple, using only Fink's classic result about the existence of Nash equilibria for <i>multi-player discounted stochastic games</i></p>

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“…There are several examples of biological networks, such as metabolic networks, protein interaction networks, neural networks, and vascular networks [27][28][29][30] . Several complex systems have been investigated recently from a networks viewpoint that link the different elements comprising them 31 .…”

Section: Introductionmentioning

confidence: 99%

Hip osteoarthritis: A novel network analysis of subchondral trabecular bone structures

Dorraki

Muratovic

Fouladzadeh

et al. 2022

Preprint

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Hip osteoarthritis (HOA) is a degenerative joint disease that leads to the progressive destruction of subchondral bone and cartilage at the hip joint. Development of effective treatments for HOA remains an open problem, primarily due to the lack of knowledge of its pathogenesis and a typically late-stage diagnosis. We describe a novel network analysis methodology for micro-computed tomography (micro-CT) images of human trabecular bone. We explored differences between the trabecular bone microstructure of femoral heads with and without HOA. Large-scale automated extraction of the network formed by trabecular bone revealed significant network properties not previously reported for bone. Profound differences were discovered, particularly in the proximal third of the femoral head, where HOA networks demonstrated elevated numbers of edges, vertices and graph components. When further differentiating healthy joint and HOA networks, the latter showed fewer small-world network properties, due to decreased clustering coefficient and increased characteristic path length. Furthermore, we found that HOA networks had reduced length of edges, indicating the formation of compressed trabecular structures. In order to assess our network approach, we developed a deep learning model for classifying HOA and control cases, and we fed it with two separate inputs: (i) micro-CT images of the trabecular bone, and (ii) the network extracted from them. The model with plain micro-CT images achieves 74.63% overall accuracy while the trained model with extracted networks attains 96.47% accuracy. We anticipate our findings to be a starting point for a novel description of bone microstructure in HOA, by considering the phenomenon from a graph theory viewpoint.

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Truels and strategies for survival

Cited by 8 publications

References 20 publications

On the Nash Equilibria of a Duel with Terminal Payoffs

On the Nash Equilibria of a Duel with Terminal Payoffs

A note on the Nash equilibria of some multi-player reachability/safety games

Hip osteoarthritis: A novel network analysis of subchondral trabecular bone structures

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