Winning?

 

Marianne

All day, all night, Marianne
Down by the seaside siftin' sand
Even little children love Marianne
Down by the seaside siftin' sand

My maternal Grandmother’s name was  Marjanna.  My sister is named Marianne.  This post is of course dedicated to them.

The icon of the French Republic is Marianne.  The comparable in the United States would be Lady Liberty.  The Motto of the French Republic is Liberté! Égalité! Fraternité!

Those who believe primarily in Liberté, Liberty, are perhaps User Optimalists.  They believe that their own Optimal is paramount.  They believe in Winning.  They think that Winning is not the thing, it is the only thing.  They believe that a Tie is like kissing your sister and that second place is first loser.  At its worst this means winning at all costs including lying, cheating, and stealing.  Because of their beliefs it is difficult to find anyone to play with them.

Those who believe primarily in Égalité, Equality, are perhaps System Optimalists.  They believe that the Optimal of the system is paramount to their own Optimal.  They think everyone should get the benefits of winning, that everyone should get a participation ribbon, that everyone should take one for the team, and that no score should be kept.  They believe that a tie should have the same value as winning.  At its worst this places no value on winning.  Because of their beliefs, System Optimalists have no incentive to produce anything if it only can be taken from them and besides, they don’t like playing anyway.

Those who believe primarily in Fraternité, Fraternity, believe in the strength of brotherhood, safety in numbers, that the whole is greater than the sum of its parts.  At its worst, they will give trust to other members of their fraternity which is not warranted, and fear anyone not in their fraternity. Because of their beliefs they are likely to want to produce value and oppose zero-sum games for at least for their own members.

Society needs all of those people. Society wants everyone to play; to produce, not only for themselves but for others.  It does so by instituting rules, which in game theory would be payout matrices.

User Optimalists would be happy with a payoff matrix, which in a classic game of two choices where you are rewarded for being different and penalized for being the same, of

		Player One
		Odd	Even
Player Two	Odd	-1	1
	Even	1	-1

System Optimalists would be happy with a payoff matrix where you were rewarded for being the same and penalized for being different, e. g.:

		Player One
		Odd	Even
Player Two	Odd	1	-1
	Even	-1	1

The problem is that while these matrices are fine for zero-sum Games, believers in Fraternity want something more than a zero-sum game, where only members of their own group can be a player, such as

		Player One
		Odd	Even
Player Two	Odd	1	1
	Even	1	1

None of these payout matrices is acceptable to all three groups.  A compromise is proposed where one choice is the preferred choice (in the example below, Odd).  It has the advantage of awarding the most points for a Win, less for a Tie, but still valuing a Tie more than a Loss, and is not a zero-sum matrix. It is  

		Player One
		Odd	Even
Player Two	Odd	0	1
	Even	2	1

But there is an interesting and simple winning strategy with this payout matrix.  A player always plays the non-preferred option in the first game.  If his opponent also chooses the non-preferred option, then that player gains a point. But if his opponent plays the preferred option, he gains no points and his opponent gains two points.  On every subsequent game with the same opponent, that player opts for whatever that opponent played in the prior game.  In this manner, if his opponent plays the preferred option again, then both players are blocked and get no points.  Let’s call this the “Tit for Tat” strategy. 

But if his opponent plays the preferred option in another game with another player, and that other player also plays the preferred option, then neither player gets any points.  Let’s call always playing the preferred option, the “Always Go For The Win” strategy. 

If person following the “Tit for Tat” strategy continues this strategy with another player who also plays the non-preferred option on his first move, they both get a point. But the “Tit for Tat” strategy gets no points in every game against players following the “Always Go For The Win” strategy.

After a large number of games have been played, players following the “Tit for Tat” strategy have the most points.  Those players may have won no games.  The “Always Go For The Win” strategy, wins more games, wins no games against those also follwing an "Always Go For The Win" stagegy, but it does not have more points. This has been tested repeatedly. https://dbeagan.blogspot.com/2021/05/tough-but-fair-beats-always-being-nasty.html

This payout matrix not only satisfies Liberty, Equality, and Fraternity, but society as a whole wins!