Application of Game Theory in the Nigerian Electoral System

Abstract: - In this paper, we carry out a study on the application of game theory in the Nigerian electoral

system. The data for the study was collected from the official publication of INEC results for six major

political parties in the February 25th, 2023 presidential election in Nigeria. In the competitive game,

each political party and INEC used mixed strategies in the game. The political parties compete for the

guidelines up to 19.99%; prosecuting electoral offenders up to 16.87%; cancelling elections up to

23.14%; inconclusive elections up to 19.19%; declaration of results up to 2.10% of the time respectively

and the value of the game was 1.5337

Key-Words: - Game theory, Electoral system, Strategies, Game value, Linear programming

Received: June 26, 2023. Revised: March 8, 2024. Accepted: April 9, 2024. Published: May 21, 2024.

Mixed strategies are the probability of applying

each of the strategies over a given number of

times. Game theory is an independent body of

knowledge that has applications across

disciplines such as mathematics, Biology,

Economics, and anything that involves

competition and rationality, see [2]. Most of

these games have only one winner after playing

and hence a two-person zero-sum game where a

loss to one is a gain to the other. Our interest is

payoffs or minimize their losses as the case may

be. The owner of the game always plays to

maximize payoff while the defender plays to

minimize losses. The defender would

concentrate on her smallest possible payoff

instead of being careless and making a loss. In

this case, the players are said to be playing their

pure strategies, and the game is expected to have

a saddle point which incidentally corresponds to

the value of the game. But if this idea of playing

the maximum row as a dominated row because

he/she wants to minimize losses. On the

contrary, the dominance rule for the owner of the

game states that the player will choose the

maximum column as a dominating column and

discard the minimum column as a dominated

column as he/she wants to maximize profit [3].

Life is an expression of Game theory in all

respects because it involves competition. In this

paper, we are interested in the Nigerian electoral

and plays the minimax criterion to maximize her

profit. At the same time, the political parties are

the defenders who also compete among

themselves and INEC. They play along the rows

of the matrix and play maximin criterion to

minimize her losses. Among the political parties,

each of these players competes for the electorates

and their votes. INEC regulates the activities of

the political parties. These set of standards are

called the strategies. The INEC strategies that

of election result. That is, INEC has six strategies

to apply to maintain law and order. Again,

political parties have six strategies such as 1.

Party structures, 2. Manifestoes, 3. Campaign, 4.

Good perception of their political parties, 5. Vote

from electorates, 6. Presentation of an acceptable

candidate for general election; therefore,

political parties have six strategies also.

INEC applies the electoral law to regulate the

activities of the political parties and the party

out these rules to guide the conduct of the

election and make it known to both the political

parties and the electorates. The electoral body

has the power to cancel any electoral process that

does not follow the electoral law or guidelines,

but the umpire has limited power over this. If the

election result was announced in compliance

with the electoral law and there was

disagreement between political parties, the

electoral body or the political party or the

mind that it is either he wins or loses value to the

opponents who are competing with him.

The authors [19] buttressed the application and

theoretical aspects of game theory as a complex

mathematical theory that aids in decision-

making. They noted that game theory is

associated with competition and rational

decision-making. The conflict situation where

players adopt all known strategies to win is a

game problem where a loss to one is a gain to the

applied between doctors and patients [20] where

each is competing with the other for a common

interest. The doctors have different strategies

such as maintaining ethical standards,

commitment to duty in other to save lives,

malpractices to make money, and other unethical

standards to cut corners, etc., the patients on the

other hand have their counter strategies to defy

the doctors’ ingenuity and in all there has to be

an equilibrium which is the value of the game.

databases such as EBSCO, Google Scholar, etc.,

and the review showed that game theory was

more popular than the entrepreneurship. This

indicates the popularity and application of game

theory in different fields of life. The author

observed that government decisions and policies

could be modelled using game theory for optimal

performance. The reviewed work shows that the

application and popularity of game theory are on

the increase. Again, similar work was done by

[22], where a bibliometric analysis of game

theory was carried out to compare the popularity

of game theory concerning energy and natural

resources. The research was based on published

works on these areas with a special interest in

WOS (Web of Science) indexing. The result

showed that game theory ranks highest in

popularity, followed by environment and green

Electoral Commission (INEC).

Nigerian presidential election of February 25,

2023.

The population of the study cut across the entire

population of adult Nigerians who took part in

the February 25, 2023 presidential election in

Nigeria. The concern of this study is on the eight

registered political parties that took part in the

presidential election.

(NNPP), All Progressive Grand Alliance

respective votes according to the official

publication of INEC will be used for the study.

In finding solutions to game theory problems,

there are about four methods that can be used.

The first is to look for saddle points if the players

are playing a pure strategy, basically when the

game is static, but in this case, it will be

impossible for political parties to apply a pure

dominance. In this case, each political party is

trying to minimize losses by playing the

minimum rows and considering the maximum

row as a dominated row while the minimum row

is a dominating row. But this game is large and

not only that no row entirely dominates the other,

we observed that no available strategy should be

ignored, otherwise, the political party will inflict

self-injuries on itself. On the other hand, INEC

is the owner of the game and stands to lose

The following are the assumptions that guided us

in the development of the Game model:

1. The cost matrix does not have a saddle point

2. No row or column dominates the other.

4. Each player has a mixed strategy to adopt.

INEC has six (6) strategies a, . . . , f and Political

Parties has six (6) strategies k, . . . , p. Table 1 is

explained as follows:

d = Cancelling election

f = Declaration of electoral result

The six Political parties’ strategies are:

k = Party structure

l = Manifestoes

n = People’s perception of the political party

o = Vote from the electorate

p = Acceptable candidate in the general election

The values of the cost matrix Xka, Xkb, . . ., Xpe,

result of the combination of the strategies.

AA = column f

Applying equation (2), we have

From equation (5), we have

From equation (7),

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Augmenting the slack variables, from equation

(6), we have

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From equation (11), the strategies for INEC are;

the primal decision variables which were

represented by yi’s, and the strategies for INEC

which were the dual decision variables were

represented by xi’s. These decision variables are

the strategies, see the summary of parties’ and

INEC’s strategies in Appendix 3. Both players

applied their mixed strategies in various

proportions. We should note that the mixed

strategies are the probabilities of applying each

strategy over a given proportion of time. The

system such as Nigeria's electoral system and

exactly applied by each player to win the

election. We also noticed from Appendix 3 that

the sum of the strategies for both political parties

and INEC is unity (that is, one) respectively.

This corresponds to the law of probability which

states that the sum of probabilities of an event is

one.

From the parties’ and INEC’s strategy summary

table in Appendix 3, we interpret as follows: The

the political parties to be successful in the

people’s perception of the political party up to

20.26% of the time; vote from electorate up to

19.54% of the time and acceptable candidate up