Politics 101 wonders who should be the next opposition leader. Specifically (since his post is short, I might as well reproduce it wholly here):

Hypothetical question: If DAP and PAS win 18 federal seats each in the elections and PKR wins one, which party would the PKR MP back for Leader of the Opposition?

Is the DAP doing enough to ensure, come what may, it will continue to hold the Opposition Leadership Office?

Is winning 18 seats and letting Mullah Hadi Awang take over the islamist agenda as Opposition Leader a victory for secularism? [Hypothetical question. Politics 101 Malaysia. February 6 2008]

This of course asked with an assumption that these parties would fail to form the next government.

If the political scenario does reach that stage, it is presumptuous for anyone of us to conclude that candidates for the next opposition leader would be either DAP or PAS. It could be from PKR. In a situation where a small party holds the tie-breaker vote, it may actually have disproportionate influence over its larger partners.

In fact, the Nash equilibrium in that situation is to have a MP from PKR to be the next opposition leader as proven in the following diagram:

Some rights reserved. By Mohd Hafiz Noor Shams.

For those unfamiliar with game theory, this is how you read the diagram.

In the payoff boxes (the ones with a pair of numbers in it), the first figure is the payoff for Player 1 (DAP) while the second figure corresponds to Player 2’s (PAS) payoff. The numbers are ordinal and not cardinal.

The first box — named P1’s optimality — shows Player 1’s (DAP) best responses given Player 2’s (PAS) action. Those responses have been highlighted in yellow.

The third box — P2’s optimality — shows Player 2’s (PAS) best responses given Player 1’s (DAP) action. Those responses have been highlighted in yellow too.

The third box highlights only overlapped responses and these responses are known as Nash equilibrium. As you can see, there is only an equilibrium.

The underlying rationale behind matrices and payoff is simple: there are 3 rules.

One is that PKR refrains from voting DAP and PAS; it only votes for itself. An either-or voting for DAP or PAS by the smaller party is bound to hurt its relationship with the two large parties. In chess, it is called zugzwang; any movement is unfavorable and the best move is not to move at all but of course, skipping a turn is not an option in chess. Unlike chess however, PKR does not need to move in this political maneuver. If PKR totally refrains from voting at all, boxes with {6,5} and {5,6} will be {0,0}. Why?

That leads us to rationale number 2: the worst outcome for all players is the lack of a leader. In the matrices, payoff {0,0} illustrates a situation of no opposition leader and that happens when both parties vote for themselves with PKR abstaining for voting.

Three, PAS and DAP hate each other gut. This is observable in payoffs {10,1} and {1,10}.

If a person plays out the coordination game, actions by both DAP and PAS that overlap with each other is to choose PKR as the opposition leader.

In case PKR totally refrains from voting, there will be three Nash equilibria. Do you know which ones?

4 Responses to “[1540] Of Nash equilibrium for DAP-PAS-PKR”

  1. on 06 Feb 2008 at 20:51 sigma

    Haha, the good ol’ Nash Eq.

    PKR would be a more powerful king-maker if the ability to decide on who would obtain the ability to form the next government fell into its hands :D

    But I guess beggars can’t be choosers now. A bit odd though, fighting for the position of Opposition Leader. All other democracies view this job as the most undesirable in politics, and here we have 3 leaders from 3 different opposition parties vying for it. Malaysian politics for you. Lol.

  2. on 06 Feb 2008 at 21:03 Hafiz Noor Shams

    Yup. Just like the Green Party in Germany not too long ago!

  3. on 10 Feb 2008 at 01:22 Elanor

    I am confused.

    Can you explain further the structure of the game? Ie,
    1. how many players are there? 2 or 3?
    2. what is the strategy space for the players?
    3. what do the payoffs represent?

    I did a game theoretic ‘analysis’ on the stable strategy for the opposition parties once, but based on their degree of cooperation and voter support base… hmmm.

  4. on 10 Feb 2008 at 12:47 Hafiz Noor Shams

    Dear Elanor,

    1. There are really 3 player. The 2 players (DAP and PAS; full player) and the 1/3 player (PKR) has just one option. PKR refrains from voting except for itself. Only DAP and PKR are shown in the table because of the assumption on PKR; that assumption allows me to just integrate PKR into the game without drawing a tree or a 3D table. (I certainly hate formulae)

    2. For DAP, the preference is DAP>PKR>PAS. For PAS, PAS>PKR>DAP. PKR’s preference is irrelevant because it has just one option. Given hostility between DAP and PAS and cooperation the two have shown to PKR, I feel the preferences are justified.

    3. The payoffs represent preferences to reflect that in #2. Or in other words, “Am I happy with it?”

    The issue which I had problem with was the assignment of preference whenever DAP chooses PKR while PAS choose DAP or PAS, and vice versa. I was tempted to put {0,0} (which leads to 3 equilibria) but I figure, I should synthesize the two rules which says DAP loves to vote for itself and no leader is the worst scenario.

    So, whenever a non-PKR player chooses PKR, the preference is itself>PKR>(the other).

    Do I made sense?

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