Tit for Tat Logical Fallacy
Classically, Tit for Tat is a math problem
With different numbers, different conclusions may be drawn.
Tit for Tat is a mathematical problem in game theory in which the
outcome for each turn is dependent upon how a player and their opponent
Each player (Player One & Player Two) decide how to
play (Nice or Mean) and they get points dependent upon how the other
The game is called Tit for Tat because the computer program that won this first program had two simple rules:
Here's a sample payoff chart (Payoff Chart #1) as was used in the original game (or close enough for our purposes).
- Play 'Nice' to start
whatever the other guy just played on your next turn ('Nice' for
'Nice' and 'Mean' for 'Mean', otherwise known as Tit for Tat)
|Payoff Table #1||Player Two:Nice||Player Two: Mean|
|Player One: Nice||Player One: 3, Player Two: 3||Player One: 0, Player Two: 5|
|Player One: Mean||Player One: 5, Player Two: 0||Player One: 1, Player Two: 1|
than doing any number crunching, I'll simply point out that Payoff
Chart #1 was arbitrarily decided upon by the game's creator.
we could play a slightly different game with a different arbitrary
payoff chart (see Payoff Chart #2) and maybe get different
|Payoff Table #2||Player Two:Nice||Player Two: Mean|
|Player One: Nice||Player One: 9, Player Two: 9||Player One: 0, Player Two: 0|
|Player One: Mean||Player One: 0, Player Two: 0||Player One: 0, Player Two: 0|
course, we don't get different results. If using Payoff Chart #1
the best strategy for both players is to play 'Nice'. And this
remains the best strategy is using Payoff Chart #2 (only hopefully
it's a lot easier to see) as playing 'Nice' is the only way for
anyont to get any points.
Here's another chart (Payoff Table #3) that makes a different winning strategy easy to see.
|Payoff Table #3||Player Two:Nice||Player Two: Mean|
|Player One: Nice||Player One: 0, Player Two: 0||Player One: 0, Player Two: 0|
|Player One: Mean||Player One: 0, Player Two: 0||Player One: 9, Player Two: 9|
Hopefully, it's pretty much a no-brainer to play 'Mean' if using Payoff Table #3.
here we perhaps get into the metaphysics of 'Nice' and 'Mean' and
realize that mathematically they mean no more than X or Y).
Anyhow, things get interesting if we change the chart again (per Payoff Table #4):
|Payoff Table #4||Player Two:Nice||Player Two: Mean|
|Player One: Nice||Player One: 0, Player Two: 0||Player One: 0, Player Two: 5|
|Player One: Mean||Player One: 5, Player Two: 0||Player One: 0, Player Two: 0|
Table #4 is interesting because the best move for each player is
to play 'Mean', but they don't get any points if the other doesn't play
'Nice' to their 'Mean'. Or in other words, the mutual winning
strategy is for one to play 'Nice' to the other's 'Mean' and then
We could further refine the table as per Payoff Table #5:
|Payoff Table #5||Player Two:Nice||Player Two: Mean|
|Player One: Nice||Player One: 1, Player Two: 2||Player One: 0, Player Two: 4|
|Player One: Mean||Player One: 8, Player Two: 0||Player One: 2, Player Two: 1|
figure out the 'winning' strategy without crunchin any numbes, all we
have to do is look at the payoff chart and figure out how Player One
scores the most and then do the same thing for Player Two. In each
case (because I designed the chart that way), each player scores the
most if they play 'Mean' to their opponent's 'Nice'. So, each
would score the highest if they alternated. Or (and this is where
it gets really interesting), Player One would wind up with the same
score as Player Two if they played thusly:
|Turn Number||Player One||Player Two|
|1||Mean: 8||Nice: 0|
|2||Nice: 0||Mean: 4|
|3||Nice: 0||Mean: 4|
|4||Nice: 0||Mean: 4|
|5||Nice: 0||Mean: 4|
|6||Mean: 8||Nice: 0|
The exact order doesn't matter, but if they cooperate, both can wind up with a score of 16 after 6 turns.
I'm not going to be happy with that, either. Because, Payer One
could wind up with 48 points (8 x 6) after 6 turns, so in truth, it
would be in both Player One & Player Two's best interest for Player
Two to let Player One win in return for some sort of payment.
Or if that's not clear, if they both split Player One's maximum
winnings equally, they could both wind up with 24 points.
of course isn't how the game of Tit for Tat is played, but this
exercise was simply to convince you why Tit for Tat proves (suggests,
implies, shows, etc) diddly squat in regards to Ultruistic Behavior
Being Inevitable. It doesn't. Tit for Tat is a math
problem. And if the problem is set up in a different way with different rules,
different outcomes and strategies become optimal.
I won't go
into these last two as deeply, but before I go, I would like to throw
out that there are at least two other arbritary aspects of Tit for Tat
that decide the outcome.
The first is that the game is of known
length (15 turns, classically, I believe). And the second is that
one is forced to continue to play against the same opponent throughout
the competition (whether one wants to or not). But if
the game's length is changed to one of of indeterminite
duration (or to as long as both parties wish to interact) and any
player may choose to switch who they play with at any time,
the optimal strategies may change. Certainly, playing
'Nice' first will fail against an opponent who plays
'Mean' in a one round competition with the classic payoff chart. And without repeated
interactions, the concept of cooperation or ultruism becomes
meaningless. But by the same token, players who are 'Mean' might
find it difficult to find partners to play with if the field is limited.
this really isn't an arguement against ultruism (it's benefits or
inevitabiltiy in human interaction). Rather (and much more
simply), the game Tit for Tat proves nothing in that regard.
It's simply a math problem. And it no more proves altruism
no more than x+y proves the existence of God.
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copyright © 2013 Brett Paufler
reach me at email@example.com
Chess may (or may not) model medieval tactical warfare.
But is certainly says (or proves) nothing about the relative merits of Knights and Bishops.In the end, Chess is just a game.As it Tit for Tat.