The good, the bad, the well-connected

In this paper, we analyse a variation of truel competitions in which each prospective player is represented by a node in a scale-free network. Without the inclusion of any particular spatial arrangement of players, traditional game theory suggests that in many truel settings the strongest player often has the lowest probability of survival, a result which has been popularised by the term survival of the unfittest. However, both our single run and the Monte-Carlo simulations suggest that this particular notion does not hold in scale-free networks. The spatial structure and arrangement of players are crucial for the outcome of truels, as in scale-free networks the number of players surviving the competition positively depends on their marksmanship (i.e. the strongest players indeed have the highest probability of survival).No sponso

Victory by the Weakest: Effects of Negative Advertising in N\u3e2 Candidate Campaigns

The truel, or three way duel, has distinct properties from duels: the weakest contestant often has a very good chance to win. This paper explores application of the logic of truels to election campaigns involving negative advertising. We show that negative campaigning that pits the leading candidates against each other can create circumstances in which the third (or worse) place candidate wins in one or more of the Nash equilibria of the game. We then study whether the simulated existence of an opportunity for Nash equilibrium victory by third place candidates predicts such outcomes in U.S. state-wide elections

The Attrition Dynamics of Multilateral War

We extend classical force-on-force combat models to study the attrition dynamics of three-way and multilateral war. We introduce a new multilateral combat model (the multiduel) which generalizes the Lanchester models, and solve it under an objective function which values one's own surviving force minus that of one's enemies. The outcome is stark: either one side is strong enough to destroy all the others combined, or all sides are locked in a stalemate which results in collective mutual annihilation. The situation in Syria fits this paradigm

On the Nash Equilibria of a Simple Discounted Duel

We formulate and study a two-player static duel game as a nonzero-sum discounted stochastic game. Players $P_{1},P_{2}$ are standing in place and, in each turn, one or both may shoot at the other player. If $P_{n}$ shoots at $P_{m}$ ($m\neq n$), either he hits and kills him (with probability $p_{n}$) or he misses him and $P_{m}$ is unaffected (with probability $1-p_{n}$). The process continues until at least one player dies; if nobody ever dies, the game lasts an infinite number of turns. Each player receives unit payoff for each turn in which he remains alive; no payoff is assigned to killing the opponent. We show that the the always-shooting strategy is a NE but, in addition, the game also possesses cooperative (i.e., non-shooting) Nash equilibria in both stationary and nonstationary strategies. A certain similarity to the repeated Prisoner's Dilemma is also noted and discussed

Последовательные труэли: равновесие с выживанием сильнейшего

A sequential truel is a generalisation of duel. This type of games is known because of the «survival of the weakest» paradox, where weakest player have the highest probability of survival. We analyse a typical variation of this model, in which players are allowed to shoot in the air. We show that there exists a SPE-equilibrium, where the strongest player, against the paradox statement, has the highest probability of survival

Techniques to Understand Computer Simulations: Markov Chain Analysis

The aim of this paper is to assist researchers in understanding the dynamics of simulation models that have been implemented and can be run in a computer, i.e. computer models. To do that, we start by explaining (a) that computer models are just input-output functions, (b) that every computer model can be re-implemented in many different formalisms (in particular in most programming languages), leading to alternative representations of the same input-output relation, and (c) that many computer models in the social simulation literature can be usefully represented as time-homogeneous Markov chains. Then we argue that analysing a computer model as a Markov chain can make apparent many features of the model that were not so evident before conducting such analysis. To prove this point, we present the main concepts needed to conduct a formal analysis of any time-homogeneous Markov chain, and we illustrate the usefulness of these concepts by analysing 10 well-known models in the social simulation literature as Markov chains. These models are: • Schelling\'s (1971) model of spatial segregation • Epstein and Axtell\'s (1996) Sugarscape • Miller and Page\'s (2004) standing ovation model • Arthur\'s (1989) model of competing technologies • Axelrod\'s (1986) metanorms models • Takahashi\'s (2000) model of generalized exchange • Axelrod\'s (1997) model of dissemination of culture • Kinnaird\'s (1946) truels • Axelrod and Bennett\'s (1993) model of competing bimodal coalitions • Joyce et al.\'s (2006) model of conditional association In particular, we explain how to characterise the transient and the asymptotic dynamics of these computer models and, where appropriate, how to assess the stochastic stability of their absorbing states. In all cases, the analysis conducted using the theory of Markov chains has yielded useful insights about the dynamics of the computer model under study.Computer Modelling, Simulation, Markov, Stochastic Processes, Analysis, Re-Implementation

Random multi-player games

The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also, local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many situations, however, interactions between different numbers of players in each round could take place, and this case cannot be reduced to pairwise interactions. In this work, we formalize and generalize the definition of evolutionary stable strategy (ESS) to be able to include a scenario in which the game is played by two players with probability p and by three players with the complementary probability 1-p. We show the existence of equilibria in pure and mixed strategies depending on the probability p, on a concrete example of the duel-truel game. We find a range of p values for which the game has a mixed equilibrium and the proportion of players in each strategy depends on the particular value of p. We prove that each of these mixed equilibrium points is ESS. A more realistic way to study this dynamics with high-order interactions is to look at how it evolves in complex networks. We introduce and study an agent-based model on a network with a fixed number of nodes, which evolves as the replicator equation predicts. By studying the dynamics of this model on random networks, we find that the phase transitions between the pure and mixed equilibria depend on probability p and also on the mean degree of the network. We derive mean-field and pair approximation equations that give results in good agreement with simulations on different networks.Fil: Kontorovsky, Natalia Lucía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaFil: Pinasco, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Vazquez, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentin

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How Trump triumphed: Multi-candidate primaries with buffoons

While people on all sides of the political spectrum were amazed that Donald Trump won the Republican nomination this paper demonstrates that Trump's victory was not a crazy event but rather the equilibrium outcome of a multi-candidate race where one candidate, the buffoon, is viewed as likely to self-destruct and hence unworthy of attack. We model such primaries as a truel (a three-way duel), solve for its equilibrium, and test its implications in a laboratory experiment. We find that people recognize a buffoon when they see one and aim their attacks elsewhere with the unfortunate consequence that the buffoon has an enhanced probability of winning. This result is strongest amongst those subjects who demonstrate an ability to best respond suggesting that our results would only be stronger when the game is played by experts and for higher stakes