- +1-530-264-8006
- info@tutorsglobe.com

18,76,764

Questions

Asked

21,311

Experts

9,67,568

Questions

Answered

Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!

Submit Assignment2015 © Tutors Globe. All rights reserved.

## One Shot Game, its Strategic Form and Eliminating Dominated Strategies

One Shot Game:If a game is played only once and the players move simultaneously or at least no player knows any of the other players’ moves before choosing his. Thus we fully characterize a one-shot game by a list of the available strategies and payoffs K = {S

_{1},.... , S_{I};π_{1},.....,π_{I}}1)

:Strategic FormIt is called the strategic (or normal) form representation of a game. For starters, let’s consider the strategic form of a one-shot game with only two players, A and B, each with two strategies, 1 and 2. (The players could be two firms, an employer and employee and a parent and child and so on.)

The payoffs for each player are collected in the following two matrices.

These are combined into a solo game matrix:

Which completely summarizes the strategic form of the game. The game matrix is useful for depicting the strategic form of games with few players (usually two or three) and a finite number of strategies.

A game is symmetric if π

_{A}^{jk}= π_{B}^{kj}for all j and k. If π_{A}^{jk}+ π_{B}^{kj }= c , where c is a constant, for each pair of strategies (j, k), then the game is constant sum; if c = 0, then it is a zero-sum game. Mostly in general games are variable sum.We are seems for a solution to such games. If each player is rational, what is her optimal strategy? This is given by the best response function. Player i’s best comeback to other player’s strategies is the solution to the following maximization problem:

max π

_{i}(s_{1},...., S_{i−1}, s_{i}, S_{i+1},....., s_{i}) ........(i)given the strategies of the (I −1) other players. Therefore the best response function is s

_{i}= R_{i}(s_{i}), which can also be expressed as Ri (s_{1},....., s_{i−1}, s_{i+1},...., s_{I}); that is, i’s most excellent strategy is generally a function of the strategies of all other players.If each player plays her optimal strategy, what happens? That is, what is the equilibrium of such a game?

2)

:Eliminating Dominated StrategiesOne feature of best response functions is that they never reflect dominated strategies. For player i, strategy si′ dominates strategy si′′ if the payoff to si′ exceeds the payoff to si ′′ for every combination of other players’ strategies si ; that is, if π i (si ′ ,si ) > π i (si ′′ ,si ) ...........(ii)

for all s

_{i}. Rational players never play dominated strategies si′′ , so we can frequently eliminate some strategies as candidates for solutions.Latest technology based Microeconomics Online Tutoring AssistanceTutors, at the

www.tutorsglobe.com, take pledge to provide full satisfaction and assurance inMicroeconomics helpviaonline tutoring. Students are getting 100% satisfaction byonline tutorsacross the globe. Here you can get homework help for Microeconomics, project ideas and tutorials. We provide email basedMicroeconomics help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Microeconomics. ThroughOnline Tutoring, you would be able to complete your homework or assignments at your home. Tutors at theTutorsGlobeare committed to provide the best qualityonline tutoringassistance forMicroeconomics Homework helpandassignment helpservices. They use their experience, as they have solved thousands of the Microeconomics assignments, which may help you to solve your complex issues of Microeconomics.TutorsGlobeassure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide thehomework helpas per the deadline or given instruction by the student, we refund the money of the student without any delay.