Databases
StackOverflow2013
Postsdbo
PO
 

Note that there are some explanatory texts on larger screens.

plurals
  1. PO
    primarykey
    data
    text
    <p>Since each player uses the same strategy described in your <code>goForBiggerResource</code> method, and you try to maximize the overall payoff, the best strategy would be three players sticking with the local resource and one player going for the big game. Unfortunately since they can not agree on a strategy, and I assume no player can not be distinguished as a Big Game Hunter, things get tricky.</p> <p>We need to randomize whether a player goes for the big game or not. Suppose p is the probability that he goes for it. Then separating the cases according to how many Big Game Hunters there are, we can calculate the number of cases, probabilities, payoffs, and based on this, expected payoffs.</p> <ul> <li>0 BGH: (4 choose 0) cases, (1-p)^4 prob, 4 payoff, expected 4(p^4-4p^3+6p^2-4p+1)</li> <li>1 BGH: (4 choose 1) cases, (1-p)^3*p prob, 5 payoff, expected 20(-p^4+3p^3-3p^2+p)</li> <li>2 BGH: (4 choose 2) cases, (1-p)^2*p^2 prob, 4 payoff, expected 24(p^4-2p^3+p^2)</li> <li>3 BGH: (4 choose 3) cases, (1-p)*p^3 prob, 3 payoff, expected 12(-p^4+p^3)</li> <li>4 BGH: (4 choose 4) cases, p^4 prob, 2 payoff, expected 2(p^4)</li> </ul> <p>Then we need to maximize the sum of the expected payoffs. Which is -2p^4+8p^3-12p^2+4p+4 if I calculated correctly. Since the first term is -2 &lt; 0, it is a concave function, and hopefully one of the roots to its derivative, -8p^3+24p^2-24p+4, will maximize the expected payoffs. Plugging it into an online polynomial solver, it returns three roots, two of them complex, the third being p ~ 0.2062994740159. The second derivate is -24p^2+48p-24 = 24(-p^2+2p-1) = -24(p-1)^2, which is &lt; 0 for all p != 1, so we indeed found a maximum. The (overall) expected payoff is the polynomial evaluated at this maximum, around 4.3811015779523, which is a 1.095275394488075 payoff per player.</p> <p>Thus the winning method is something like this</p> <pre><code>private static boolean goForBiggerResource () { return Math.random() &lt; 0.2062994740159; } </code></pre> <p>Of course if players can use different strategies and/or play against each other, it's an entirely different matter.</p> <p>Edit: Also, you can cheat ;)</p> <pre><code>private static int cheat = 0; private static boolean goForBiggerResource () { cheat = (cheat + 1) % 4; return cheat == 0; } </code></pre>
    singulars
    1. This table or related slice is empty.
    1. POSolving a simple maximization game
      singulars
      1. PTQuestion
    1. PTAnswer
    1. USFrigo
    1. USFrigo
    plurals
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. POSolving a simple maximization game
      singulars
      1. PTQuestion
    1. This table or related slice is empty.
    1. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    3. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    1. COlol, the point was not to make it cheatproof ; ) That said... I made it on purpose that player had to use the same strategy (so no cheating) and based on the answer talking about the Nash equilibrium from what I understand that's kinda the entire point of reaching the Nash equilibrium: there **is** only one Nash equilibrium and both you and the other person found it. The wikipedia explains that players will play optimally knowing that other players will play optimally too: so to reach the equilibrium player will end up using the strategy you guys both pointed out.
      singulars
      1. PO
      1. USCedric Martin
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload