Original scientific paper A zero-sum game approach for H∞ robust control of continuous-time singularly perturbed bilinear quadratic systems with an additive disturbance input is presented. By regarding the stochastic disturbance (or the uncertainty) as "the nature player", the H∞ robust control problem is transformed into a twoperson zero-sum dynamic game model. By utilizing the singular pertur...

Finding Nash equilibrium in a two-player normal form game (2-Nash) is one of the most extensively studied problem within mathematical economics as well as theoretical computer science. Such a game can be represented by two payoff matrices A and B, one for each player. 2Nash is PPAD-complete in general, while in case of zero-sum games (B = −A) the problem reduces to LP and hence is in P. Extendi...

A complex system exhibiting uncertainty as well randomness may be portrayed by an uncertain random singular difference equation. This paper investigates two-person nonzero-sum and zero-sum games based on equations. First, approach is proposed to translate the game into equivalent for a standard dynamic system. The relevant recursive equations are developed search Nash equilibrium converted game...

Deterrence has been a crucial element in fighting terrorism, both in actual politics and rational choice analyses of terrorism. But there are superior strategies to deterrence. One is to make terrorist attacks less attractive. Another to raise the opportunity cost – rather than the material cost – to terrorists. These alternative strategies effectively dissuade potential terrorists. The strateg...

We consider a large community of individuals who mix strongly and meet in pairs to bet on a coin toss. We investigate the asset distribution of the players involved in this zero-sum repeated game. Our main result is that the asset distribution converges to the exponential distribution, irrespective of the size of the bet, as long as players can never go bankrupt. Analytical results suggests tha...

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...

We introduce a method of decomposing a p-player normal form game into 2p simultaneously-played component games, each distinguished by the set of “active” players whose choices influence payoffs. We then prove that a normal form game is a potential game if and only if in each of the component games, all active players have identical payoff functions, and that in this case, the sum of these share...

Lines of Action (LOA) is a two-person zero-sum game with perfect information; it is a chess-like game with a connection-based goal. In this note the 6 × 6 variant of LOA is weakly solved. A Proof-Number search method, PN, is used to compute that the game is a win for the first player (Black). Based on the results of solving the boards up to 6× 6, an optimistic time frame is given for solving 7×...