Pure Strategy Nash Equilibrium in 2-Contestant Generalized Lottery Colonel Blotto Games

2021 ◽  
Author(s):  
Xinmi Li ◽  
Jie Zheng
Keyword(s):  
Nash Equilibrium ◽  
Pure Strategy ◽  
Colonel Blotto ◽  
Colonel Blotto Games ◽  
Strategy Nash Equilibrium

ON COURNOT COMPETITION UNDER RANDOM YIELD

2013 ◽  
Vol 30 (04) ◽  
pp. 1350007 ◽  
Author(s):  
XIAOMING YAN ◽  
YONG WANG
Keyword(s):  
Nash Equilibrium ◽  
Production Cost ◽  
Pure Strategy ◽  
Cournot Competition ◽  
Random Yield ◽  
Cournot Model ◽  
Random Capacity ◽  
Strategy Nash Equilibrium

We look at a Cournot model in which each firm may be unreliable with random capacity, so the total quantity brought into market is uncertain. The Cournot model has a unique pure strategy Nash equilibrium (NE), in which the number of active firms is determined by each firm's production cost and reliability. Our results indicate the following effects of unreliability: the number of active firms in the NE is more than that each firm is completely reliable and the expected total quantity brought into market is less than that each firm is completely reliable. Whether a given firm joins in the game is independent of its reliability, but any given firm always hopes that the less-expensive firms' capacities are random and stochastically smaller.

A Note on a Comparison of Simultaneous and Sequential Colonel Blotto Games

2012 ◽  
Vol 18 (3) ◽  
Author(s):  
Yumiko Baba
Keyword(s):  
Nash Equilibrium ◽  
Theoretical Prediction ◽  
Cyber Terrorism ◽  
Attack Pattern ◽  
Period 2 ◽  
Blotto Game ◽  
Irrational Behavior ◽  
Theoretical Predictions ◽  
Colonel Blotto ◽  
Colonel Blotto Games

Abstract Clark and Konrad (2007) introduce the weakest link against the best shot property to the Colonel Blotto game where the defendant has to win all the battle fields while the attacker only needs to win at least one battlefield. They characterize the Nash equilibrium assuming that the attacker attacks all the battlefields simultaneously. We construct a two stage model and endogenize the attacker’s attack pattern. We show that the attacker chooses a sequential attack pattern in the subgame perfect Nash equilibrium. Therefore, the game analyzed by Clark and Konrad (2007) is never realized. We also conducted experiments and found that the subjects’ behavior was inconsistent to theoretical predictions. Both players overinvested and the variances were large. In the simultaneous game, the attackers took a guerrira strategy at 30% of the time in which they invested only in one battlefield and the defenders took a surrender strategy at 11% of the time in which they invested nothing in the simultaneous game. Both players invested more in period 1 than in period 2 in the sequential game. Although all of these are inconsistent to the theoretical predictions, the winning probability of a game was consistent to the theoretical prediction in the simultaneous games, but it was lower than the theoretical prediction in the sequential games. We conclude that the subjects’ irrational behavior is mainly a rational response to his/ her opponent’s irrational behavior. Our model can explain terrorism, cyber terrorism, lobbying, and patent trolls and the huge gap between the theory and the experiments are important considering the significance of the problems.

Finding the Pure-Strategy Nash Equilibrium Using a Fixed-Point Algorithm

2013 ◽  
Vol 427-429 ◽  
pp. 1803-1806 ◽  
Author(s):  
Zheng Tian Wu ◽  
Chuang Yin Dang ◽  
Chang An Zhu
Keyword(s):  
Fixed Point ◽  
Nash Equilibrium ◽  
Normal Form ◽  
Pure Strategy ◽  
Payoff Function ◽  
Fixed Point Algorithm ◽  
Linear Programming Formulation ◽  
Active Research ◽  
Person Game ◽  
Strategy Nash Equilibrium

It is well known that determining whether a finite game has a pure-strategy Nash equilibrium is an NP-hard problem and it is an active research topic to find a Nash equilibrium recently. In this paper, an implementation of Dang's Fixed-Point iterative method is introduced to find a pure-strategy Nash equilibrium of a finite n-person game in normal form. There are two steps to find one pure-strategy Nash equilibrium in this paper. The first step is converting the problem to a mixed 0-1 linear programming formulation based on the properties of pure strategy and multilinear terms in the payoff function. In the next step, the Dangs method is used to solve the formulation generated in the former step. Numerical results show that this method is effective to find a pure-strategy Nash equilibrium of a finite n-person game in normal form.

scholarly journals The Political Economy of Coalition in Indonesia

2016 ◽  
Vol 1 (1) ◽  
Author(s):  
Muhammad Ryan Sanjaya
Keyword(s):  
Political Economy ◽  
Nash Equilibrium ◽  
Political Parties ◽  
Cooperative Game ◽  
Pure Strategy ◽  
The Political ◽  
Political Bargaining ◽  
President Elect ◽  
Bargaining Table ◽  
Strategy Nash Equilibrium

Politics as an art of bargaining has gain prominent momentum following the victory of the president-elect Joko Widodo in Indonesia in 2014. This paper estimates the value of political parties under uncertainties over two possible coalitions: the Great Indonesia Coalition (Koalisi Indonesia Hebat, KIH) that supports Joko Widodo, and the Red & White Coalition (Koalisi Merah Putih, KMP) that supports Prabowo Subianto, the president candidate from the Gerindra Party. The estimation shows that the Golkar, the second largest earner of seats in the parliament, is more valuable for KMP, making them expensive to be maintained within this coalition. It suggests that the best choice for Golkar is to jump to KIH, unless the KMP provides substantial payoff to lure this party. Nonetheless, the pure strategy Nash equilibrium in a non-cooperative game of political bargaining shows that even though a party has small fair values, but it still has decisive impact in the bargaining table of a coalition.

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