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Register a new userOptimal equilibria of the best shot game
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We consider any network environment in which the best shot game is played. This is the case where the possible actions are only two for every node (0 and 1), and the best response for a node is 1 if and only if all her neighbors play 0. A natural application of the model is one in which the action 1 is the purchase of a good, which is locally a public good, in the sense that it will be available also to neighbors. This game typically exhibits a great multiplicity of equilibria. Imagine a social planner whose scope is to find an optimal equilibrium, i.e. one in which the number of nodes playing 1 is minimal. To find such an equilibrium is a very hard task for any non-trivial network architecture. We propose an implementable mechanism that, in the limit of infinite time, reaches an optimal equilibrium, even if this equilibrium and even the network structure is unknown to the social planner.
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Suppose that an $m$-simplex is partitioned into $n$ convex regions having disjoint interiors and distinct labels, and we may learn the label of any point by querying it. The learning objective is to know, for any point in the simplex, a label that occurs within some distance $epsilon$ from that point. We present two algorithms for this task: Constant-Dimension Generalised Binary Search (CD-GBS), which for constant $m$ uses $poly(n, log left( frac{1}{epsilon} right))$ queries, and Constant-Region Generalised Binary Search (CR-GBS), which uses CD-GBS as a subroutine and for constant $n$ uses $poly(m, log left( frac{1}{epsilon} right))$ queries. We show via Kakutanis fixed-point theorem that these algorithms provide bounds on the best-response query complexity of computing approximate well-supported equilibria of bimatrix games in which one of the players has a constant number of pure strategies. We also partially extend our results to games with multiple players, establishing further query complexity bounds for computing approximate well-supported equilibria in this setting.
A new model of collusions in an organization is proposed. Each actor $a_{i=1,cdots,N}$ disposes one unique good $g_{j=1,cdots,N}$. Each actor $a_i$ has also a list of other goods which he/she needs, in order from desired most to those desired less. Finally, each actor $a_i$ has also a list of other agents, initially ordered at random. The order in the last list means the order of the access of the actors to the good $g_j$. A pair after a pair of agents tries to make a transaction. This transaction is possible if each of two actors can be shifted upwards in the list of actors possessed by the partner. Our numerical results indicate, that the average time of evolution scales with the number $N$ of actors approximately as $N^{2.9}$. For each actor, we calculate the Kendalls rank correlation between the order of desired goods and actors place at the lists of the goods possessors. We also calculate individual utility funcions $eta_i$, where goods are weighted according to how strongly they are desired by an actor $a_i$, and how easily they can be accessed by $a_i$. Although the individual utility functions can increase or decrease in the time course, its value averaged over actors and independent simulations does increase in time. This means that the system of collusions is profitable for the members of the organization.
In nature and society problems arise when different interests are difficult to reconcile, which are modeled in game theory. While most applications assume uncorrelated games, a more detailed modeling is necessary to consider the correlations that influence the decisions of the players. The current theory for correlated games, however, enforces the players to obey the instructions from a third party or correlation device to reach equilibrium, but this cannot be achieved for all initial correlations. We extend here the existing framework of correlated games and find that there are other interesting and previously unknown Nash equilibria that make use of correlations to obtain the best payoff. This is achieved by allowing the players the freedom to follow or not to follow the suggestions of the correlation device. By assigning independent probabilities to follow every possible suggestion, the players engage in a response game that turns out to have a rich structure of Nash equilibria that goes beyond the correlated equilibrium and mixed-strategy solutions. We determine the Nash equilibria for all possible correlated Snowdrift games, which we find to be describable by Ising Models in thermal equilibrium. We believe that our approach paves the way to a study of correlations in games that uncovers the existence of interesting underlying interaction mechanisms, without compromising the independence of the players.
Sports are spontaneous generators of stories. Through skill and chance, the script of each game is dynamically written in real time by players acting out possible trajectories allowed by a sports rules. By properly characterizing a given sports ecology of `game stories, we are able to capture the sports capacity for unfolding interesting narratives, in part by contrasting them with random walks. Here, we explore the game story space afforded by a data set of 1,310 Australian Football League (AFL) score lines. We find that AFL games exhibit a continuous spectrum of stories rather than distinct clusters. We show how coarse-graining reveals identifiable motifs ranging from last minute comeback wins to one-sided blowouts. Through an extensive comparison with biased random walks, we show that real AFL games deliver a broader array of motifs than null models, and we provide consequent insights into the narrative appeal of real games.
In this paper, we study the role of degree mixing in the naming game. It is found that consensus can be accelerated on disassortative networks. We provide a qualitative explanation of this phenomenon based on clusters statistics. Compared with assortative mixing, disassortative mixing can promote the merging of different clusters, thus resulting in a shorter convergence time. Other quantities, including the evolutions of the success rate, the number of total words and the number of different words, are also studied.
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