Gentleman, Java

import static java.lang.Integer.parseInt;
import java.io.*;
import java.util.*;

public class Gentleman{
    private final static String FILE_NAME = "data/Mimicer.txt";

    static {
        new File("data").mkdir();
    }

    public static void main(String[] args) throws Exception{
        int totalCake = parseInt(args[0]);
        int cakeLeft = parseInt(args[1]);
        int totalPeople = parseInt(args[2]);
        int peopleLeft = parseInt(args[3]);

        if (totalCake == cakeLeft){
            System.out.println(cakeLeft);
        } else {
            int previousCake = load();
            int cakeDiff = previousCake - cakeLeft;

            if (cakeDiff > optimal(previousCake, peopleLeft + 1)){
                System.out.println(peopleLeft == 1 ? cakeLeft : Math.min(cakeLeft, cakeDiff));
            } else {
                System.out.println(cakeLeft);  //Hey, I might get lucky :)
            }
        }
        save(cakeLeft);
    }

    private static void save(int cake) throws Exception{
        PrintStream out = new PrintStream(FILE_NAME);
        out.print(cake);
    }

    private static int load() throws Exception{
        Scanner in = new Scanner(new File(FILE_NAME));
        return in.nextInt();
    }

    private static int optimal(int cake, int people){
        return (cake + people - 1) / people;
    }
}

He waits for people who eat a fair share or less before he eats any cake. To prevent the greedy from getting extra cake, he takes as large a portion as possible.