Brief introduction to Game Theory

South African Politics : A case study

17 June 2024

Goals: Introduce game theory, nash equilibrium, prisoners dilemma, rational thinking

Show relevance to a current topic, South African Elections.

This is not a lecture about politics.

"African societies are like badly managed football teams, where players, because of personal rivalries, will not pass the ball in case someone scores."- Daniel Etounga-Manguelle.

Game theory is the study of mathematical models of strategic interaction among rational decision-makers. It has applications in all fields of social science, especially Economics. Originally, it addressed zero-sum games, but widened to non zero sum games.

Von Neuman and Morgenstein, Princeton 1953

Nash Equilibrium

Made famous by the movie A Beautiful Mind

Simply put - In a Nash Equilibrium participants don't get what they want, but do get the best they can

Three guys in a bar

Could have been the night of their lives if they had behaved rationally.

The Prisoners Dilemma

Three of us have broken into a house and stashed the loot. We get caught by the cops and put into separate cells. Our lawyers tell us, they have not found the loot. We are fine if none of us talk. We each get one year for damage to property. That is three years time served in total. Cop comes in and tells us each of us if we confess he will get one of us off on a plea bargain. The other two will do five years for theft. Ten years in total served.

Optional Workshop

Divide the class into groups of two and three. Each plays the role of prisoners, See how many grassed, See if the rate differs from groups of two or groups of three.

South African Elections

2 June 2024

In empirical studies the majority of prisoners talk! It gets even worse if the three prisoners each blame each other. Good cop wins.

Now apply it in real life. ANC is good cop, DA, EFF and MK are the prisoners. Instead of taking one year to get over our differences, and sweep the ANC out of power, DA bursts into tears and confesses. EFF and MK will spend five years in red and orange overalls. In the prisoners dilemma it is usually best to be the first to confess. Until you find that good cop breaks his word...

Now take a step back, stop looking at the blonde, and consider that the ONLY coalition that can actually take South Africa forward, The golden coalition of DA, EFF, MK (47%) and 4% of a minority party. (51%).

Of the relevant parties, only the ANC, IFP and PA made no demands. The DA, MK, EFF made pre talk Demands

The result was clear. ANC and IFP got more than they deserved. The DA got less that they deserved, MK and EFF got what they deserved.

The SA negotiations did not result in the Nash Equilibrium

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