Basic Implementation of Game Theory's Minimax

// pure strategy: [[2,4],[6,5]]
// mixed strategy: [[3,1],[2,4]]
 
var gameMatrix = [[2,4],[6,5]];
var rowCount = gameMatrix.length;
var columnCount = gameMatrix[0].length;
 
// an accuracy measure; anymore than 1000 will crash modern browsers
var steps = 1000;
 
// mutual payoff function
 
function M(u, s) {
	var expectedPayoff = 0;
 
	for(var i = 0; i < rowCount; i++) {
		for(var j = 0; j < columnCount; j++) {
			expectedPayoff += u[i] * s[j] * gameMatrix[i][j];
		}
	}
 
	return expectedPayoff
}
 
var insideMin = 100000, outsideMax = -100000;
var nashEquilibrium = [[], []];
 
// minimax implementation (i.e. finding security value)
 
for(x = 0; x < steps + 1; x++) {
	for(y = 0; y < steps; y++) {
		var prevMin = insideMin;
		var payoff = M([x/steps, 1-x/steps], [y/steps, 1-y/steps])
		insideMin = Math.min(insideMin, payoff);
 
		// this is for recording the nash equilibrium value
		// a new local min != a global maximum; must check both
		if(prevMin != insideMin && outsideMax != Math.max(insideMin, outsideMax)) {
			nashEquilibrium[1] = [y/steps, 1-y/steps];
		}
	}
 
	var prevMax = outsideMax;
	outsideMax = Math.max(insideMin, outsideMax);
 
	if(prevMax != outsideMax || outsideMax == insideMin) {
		nashEquilibrium[0] = [x/steps, 1-x/steps];
	}
 
	// reset the local minimum
	insideMin = 100000;
}
 
document.write('minimax: ' + outsideMax + "<br/>" +
  'nash eq: ((' +
	nashEquilibrium[0][0] + ", " + nashEquilibrium[0][1] + "), (" +
	nashEquilibrium[1][0] + ", " + nashEquilibrium[1][1] + "))"
);