The Nash equilibria of a two-person, non-zero-sum game are the solutions of a certain linear complementarity problem (LCP). In order to use this for solving a game in extensive form, the game must first be converted to a strategic description such as the normal form. The classical normal form, however, is often exponentially large in the size of the game tree. If the game has perfect recall, a ...

We present a game-theoretic account of irrational agent behavior and define conditions under which irrational behavior may be considered quasi-rational. To do so, we use a 2-player, zero-sum strategic game, parameterize the reward structure and study how the value of the game changes with this parameter. We argue that for any “underdog” agent, there is a point at which the asymmetry of the game...

The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new spin: building nim. With given finite numbers of tokens and stacks, this two-player game is played in two stages (thus belonging to the same family of games a...

Open list proportional representation is an election mechanism used in many elections, including the 2012 Hong Kong Legislative Council Geographical Constituencies election. In this paper, we assume that there are just two parties in the election, and that the number of votes that a list would get is the sum of the numbers of votes that the candidates in the list would get if each of them would...