Game Theory Assignment: Analyzing Simultaneous and Sequential Games

This assignment solution delves into game theory, specifically focusing on simultaneous and sequential games. The solution begins by analyzing a simultaneous game between two firms, where each firm chooses to either expand or not expand. The analysis includes constructing a payoff matrix to determine the optimal strategies and identify the Nash equilibrium. The solution then progresses to a sequential game, where one player moves after considering the other player's move. The solution uses backward induction to determine the optimal strategies and find the equilibrium in this sequential setting. The assignment highlights the importance of strategic decision-making and understanding the interactions between players in different game scenarios.

Running Head: Game theory
Solving Simultaneous and Sequential Games to get the Nash Equilibrium
By (Name)
(Tutor)
(University)
(Date)

Game theory 2
Solving Simultaneous and Sequential Games to get the Nash Equilibrium
Question 1
In this case there are two players who are practicing simultaneous games meaning that they are
choosing at the same time (Gallego, 2017). Both firms have two strategies; either to expand or
not expand. The outcome of the game is represented on a normal form as follows;
Firm B
Firm A
Expand No Change
Expand 50,20 85,25
No change 70,40 95,30
The above is a representation of the gain that each firm receives from employing either of the
strategies
If both firm A and B choose to Expand firm A will have a payoff of 50 and firm B a payoff of
20; thus firm A will have an advantage.
If both does not change, firm A will have a payoff of 95 and firm B a payoff of 30; thus firm A
will again have an advantage.
If firm A choose to expand, firm B will compare 20, and 25 and will choose not to change.
If firm A choose not to change, firm B will compare 40, and 30 and will choose to expand.
If firm B choose to expand, firm A will compare 50, and 70 and will choose not to change.
If firm B choose not to change, firm A will compare 85, and 95 and will choose not to change.
The optimal strategy (Firm A, Firm B) = (No change, No change)
Firm A has a dominant strategy of no Change.
Question 2
In this case there are two players, the strategies are two but the movement is sequential meaning
that one player only moves after considering the move made by the other player (Munoz-Garcia
and Toro-Gonzalez, 2016). The two strategies are Expand (E) and No change (N).
The first player has two strategies (E, N)
The second player has four contingent strategies (EE, EN, NE, NN)
The strategies for player B are represented in the normal formal as follows;

Game theory 3
Firm B
Firm A
EE EN NE NN
E 50,20 50,20 85,25 85,25
N 70,40 95,30 70,40 95,30
The following reduces to this form after backward induction;
Firm A
E N
( 85
25 ) ( 70
40 )
Firm A’S choice will be based on 85 and 70 (it will choose 85). In this case 85 gives the optimal
choice.
Equilibrium [A, B] = [Expand, No change]

Game theory 4
References
Gallego, L. (2017). Game theory II: Simultaneous games. [Online] Policonomics.com. Available
at: http://policonomics.com/lp-game-theory2-simultaneous-game/ [Accessed 10 Aug. 2018].
Munoz-Garcia, F. and Toro-Gonzalez, D. (2016). Strategy and Game Theory: Practice Exercises
with Answers. Cham: Springer International Publishing.