The concept of cognitive hierarchy (Camerer et.al (2004)) is extended to multistage games. In a multi-stage game we will assume that the rationality level of a player indicates the number of stages of the game where he puts cognitive effort to calculate optimal actions. A player of rationality level k plays optimaly in the last k stages of the game and randomizes uniformly in the first m − k, w...

The value 1 problem is a natural decision problem in algorithmic game theory. For partially observable Markov decision processes with reachability objective, this problem is defined as follows: are there strategies that achieve the reachability objective with probability arbitrarily close to 1? This problem was shown undecidable recently. Our contribution is to introduce a class of partially ob...

We solve a family of quadratic Diophantine equations associated with a simple kind of game. We show that the ternary case, in many ways, is the most interesting and the least arbitrary member of the family. 1. The Matching Games An (n, d)-matching game (n, d ≥ 2) is a game in which the player draws d balls from a bag of balls of n different colors. The player wins if and only if the balls drawn...

Hamiache’s recent axiomatization of the well-known Shapley value for TU games states that the Shapley value is the unique solution verifying the following three axioms: the inessential game property, continuity and associated consistency. Driessen extended Hamiache’s axiomatization to the enlarged class of efficient, symmetric, and linear values, of which the Shapley value is the most important...

Assume G is a graph, and k,d,m are natural numbers. The d-defective (k,m)-painting game on played by two players: Lister Painter. Initially, each vertex has k tokens uncolored. In round, chooses set M of vertices removes one token from chosen vertex. Painter colors subset X which induces subgraph G[X] maximum degree at most d. A v fully colored if received m colors. wins the end some there with...

This paper considers the advertising, pricing, and service decisions simultaneously to coordinate the supply chain with a manufacturer and a retailer. The amount of market demand is influenced by advertising, pricing and service decisions. In this paper, three well-known approaches to the game theory, including the Nash, the Stackelberg-retailer, and the cooperative game are exploited to study ...

This internship thesis intends to facilitate cognitive experiments for gameplay experience studies. To achieve this a psychophysiological logging framework was developed, which automatically reports the occurrence of specific game events to a log file and to the parallel port. Via the parallel port the communication with psychophysiological systems is possible. Thus, psychophysiological data ca...

Background: Smartphone addiction is a serious growing problem with similarities to game addiction and even drug addiction. Nowadays, a large number of Iranian children and teenagers find themselves addicted to their smartphones. This type of addiction has a serious impact on mental health among mothers. This study aimed to compare depression and rumination scores among employed and unemployed m...

We study Maker/Breaker games on the edges of the complete graph, as introduced by Chvátal and Erdős. We show that in the (m : b) game played on KN , the complete graph on N vertices, Maker can achieve a Kq for q = ( m log 2 (b+1) − o(1) ) · log2 N , which partially solves an open problem by Beck. Moreover, we show that in the (1 : 1) game played on KN for a sufficiently large N , Maker can achi...

We study Maker/Breaker games on the edges of the complete graph, as introduced by Chvátal and Erdős. We show that in the (m : b) clique game played on KN , the complete graph on N vertices, Maker can achieve a Kq for q = ( m log 2 (b+1) − o(1) ) · logN , which partially solves an open problem by Beck. Moreover, we show that in the (1:1) clique game played on KN for a sufficiently large N , Make...