Analysing "Minority Rule"
Exploring Game Theory and Mechanism Design with "Liar Game"
Liar Game is a Japanese psychological thriller manga series.
The story revolves around a tournament - The Liar Game - where contestants are each given 100 million yen and made to compete in a series of games to win the money of other players.
Losers are saddled with a 100 million yen debt.
One of the games played in Liar Game is the minority rule.
Rules of the Game
First, a player is selected at random to ask any question as long as the answer is "yes" or "no". Questions could be anything like “Am I a girl”?
Each player then votes "yes" or "no". Players can decide whether to answer honestly, but they are not allowed to select both options.
Those who vote for the "majority" answer will be eliminated from the game.
When there is a tie between "Yes" and "No", a new question is asked and voting is repeated.
Winners are players on the minority side or the less popular answer.
The minority rule game references the concept of minority game, a variation of the El Farol Bar problem in game theory.
In the El Farol Bar problem, the people of a city want to have fun at a bar. Unfortunately, if more than 60% of the population visit the bar, they will not have a good time. And if no one went to the bar, no one would have any fun. The only way to benefit in this case is to be on the minority side. That is staying at home when the bar is crowded, or visiting the bar when it is not crowded.
However, everyone must decide at the same time whether to go or not, with no knowledge of others' choices.
The Minority Game is a simple model for the collective behaviour of agents in an idealized situation where they have to compete through adaptation for a finite resource. In the El Farol Bar problem, the finite resource is “fun”.
Liar Game’s minority rule introduces the human element of cooperation to solve this problem and achieve incentive compatibility. Here, players are given a time limit to converse with others and work out strategies. If they don’t vote within that time limit, they are eliminated.
In game theory, co-operative games are games where players are convinced to adopt a particular strategy through interactions and agreements with other players.
The protagonists, Akiyama Shinichi and Nao Kanzaki form a team of players and split evenly into groups who answer “yes” and “no” with the promise that whoever ends up in the minority would split the reward with the rest of the team.
The game continues till the last round with just 4 players left and Akiyama representing his team.
Akiyama immediately announces to everyone that he will vote yes to any question asked and proceeds to vote.
There are only three contestants left to vote, so the next player must vote no to remain in the minority.
Unfortunately, all three remaining contestants would try to vote no to be the minority which will lead Akiyama to end up the minority (with his yes vote) and win the game.
Finally, the remaining players attempt to cooperate and plan their votes so the game can end in a draw. However, Akiyama is revealed to have previously confided in and struck a deal with one of the remaining 3 players who votes in his favour and he wins.
Liar Game’s minority rule shows how much impact cooperation between adversaries can make in game theory.
Excellent writing
Interesting topic, good read.