History:
Though touched on by earlier mathematical results, modern game theory
became a prominent branch of mathematics in the 1940s, especially
after the 1944 publication of The Theory of Games and Economic Behavior
by John von Neumann and Oskar Morgenstern. This profound work contained
the method -- alluded to above -- for finding optimal solutions
for two-person zero-sum games.
Around 1950, John Nash developed a definition of an "optimum" strategy for multi-player games where no such optimum was previously defined, known as Nash equilibrium. Reinhard Selten with his ideas of trembling hand perfect and subgame perfect equilibria further refined this concept. These men won The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel (also known as The Nobel Prize in Economics) in 1994 for their work on game theory, along with John Harsanyi who developed the analysis of games of incomplete information.
Research into game theory continues, and there remain games which produce counter-intuitive optimal strategies even under advanced analytical techniques like trembling hand equilibrium. One example of this occurs in the Centipede Game, where at every decision players have the option of increasing their opponents' payoff at some cost to their own.
Some experimental tests of games indicate that in many situations people respond instinctively by picking a 'reasonable' solution or a 'social norm' rather than adopting the strategy indicated by a rational analytic concept. The finding of Conway's number-game connection occurred in the early 1970s.
Applications in gambling games:
The mathematics of game theory have found their way back from the
academic world into the strategic setting on which they were originally
modelled. It is now very common, for the top Poker players to resort
to a mixed strategy (calculated as a Nash equilibrium against all
possible opposing strategies) as a defense against a more 'intuitive'
opponent. This approach was first advocated by David Sklansky in
"Theory of Poker", which drew very heavily from the work
of game theorists in economics. In order to blunt the advantage
in "reading" a player which a world champion card player
might use against him, Sklansky advocated an optimal mixed strategy
(using natural randomness) for various strategic decisions in gambling
such as:
- Bluffing & Semi-bluffing in seven card stud.
- Occasionally folding a weak hand for a final bet in limit texas holdem.
- Backgammon doubling strategy.
