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We study a generalization of hide and seek game of von Neumann [14], where each player has one or more resources. We characterize the value and Nash equilibria of such games in terms of their unidimensional marginal distributions. We propose a \(\mathcal {O}(n \log (n))\) time algorithm for computing unidimensional marginal distributions of equilibrium strategies and a quadratic time algorithm for computing mixed strategies given the margins. The characterization allows us to establish a number of interesting qualitative features of equilibria.

We study Nash equilibria of a symmetric Colonel Blotto and Colonel Lotto games. In these game two players, with \(N \ge 1\) units of resources each, distribute their resources simultaneously across \(K \ge 2\) battlefields. We introduce a characteristic of equilibria in this game called spectrum which stands for the fraction of battlefields receiving given numbers of units. We provide complete characterization of spectra of Nash equilibria in Colonel Lotto game as well as necessary conditions on spectra of Nash equilibria in Colonel Blotto game for the case of \({K}\! \mid \!{N}\).

We consider the Hotelling-Downs model with n 2 oce seeking candidates and runo voting. We show that Nash equilibria in pure strategies always exist and that there are typically multiple equilibria, both convergent (all candidates are located at the median) and divergent (candidates locate at distinct positions), though only divergent equilibria are robust to free entry. Moreover, two-policy equilibria exist under any distribution of voters’ ideal policies, while equilibria with more than two policies exist generically but under restrictive conditions that we characterize.

Two players are endowed with resources for setting up N locations on K identical circles, with N greater than K which is greater or equal 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival's. They face a resource mobility constraint such that not all N locations can be placed in the first round. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that for K = 1, the second mover always has a winning strategy in this game. In this paper we show that with K > 1, the second mover advantage disappears as in this case both players have a tying strategy. We also study a natural variant of this game where the resource mobility constraint is more stringent so that in each round each player chooses a single location where we show that the second mover advantage re-appears. We suggest some Nash equilibrium configurations of locations in both versions of the game.

We consider the Hotelling-Downs model with n ≥ 2 office seeking candidates and runoff voting. We show that Nash equilibria in pure strategies always exist and that there are typically multiple equilibria, both convergent (all candidates are located at the median) and divergent (candidates locate at distinct positions), though only divergent equilibria are robust to free entry. Moreover, two-policy equilibria exist under any distribution of voters' ideal policies, while equilibria with more than two policies exist generically but under restrictive conditions that we characterize. In this sense, our analysis suggests that two-policy equilibria are the most prominent outcomes.

In this paper we study a model of political competition where citizens vote sincerely and candidates may be either citizens or Downsian politicians. The model extends the citizen-candidate model proposed by Osborne and Slivinski [1996] by including Downsian politicians similar to those studied by Osborne [1993]. We give necessary and sufficient conditions for existence, together with complete characterisation, of one party and two party Nash equilibria in our model. An important feature, in view of the Duverger's Law, of the two-party equilibrium is that these equilibria cannot have any Downsian contestant. Moreover, we compare our model with that studied by Osborne and Slivinski [1996], showing that in both cases there exist po- litical configurations that can appear in one of the models only. We show also that in our settings it is possible to have Nash equilibria with Downsian candidates, without requiring to have very restrictive constraints on the dis- tribution function. We also argue that as the number of parties in equilibrium increases, the `likelihood' of an ideology driven citizen-candidate winning the elections and running the government falls. Finally we argue that in any equilibrium extremist parties proposing their policies uniquely are typically ideology-driven as well.