It’s very tempting to want to pay the extra $2 to secure the book even though it’s not beneficial.
@PunmasterSTP2 жыл бұрын
Stag hunt? More like "Spectacular, I bet!" Thanks for another great puzzle.
@alex_zetsu2 жыл бұрын
I guess this is a great example of how important it is to know what all the other players value. if you don't know their payoffs, or at least the probability distribution of their payoffs (like your interim dominance example of one player either being a prisoners dilemma type or a stag hunt type but the other guy at least knows the probability), it becomes difficult to come up with the optimal tactic.
@Math.Bandit2 жыл бұрын
I think in this case it likely trends towards the 20-20 equilibrium, since the row-player has a preference for that. If the column-player picks 20$, then obviously the row player prefers to get 4$ EV vs 0$ EV, but the gap between $9 EV and $8 EV if the column-player picks $10 is much smaller.
@Velzen52 жыл бұрын
Whom does one love more, a stranger or the auction house"?
@kroppraven418 Жыл бұрын
Thank you
@Markd3152 жыл бұрын
I would simply write a contract where $10 are held in escrow from each bidder and forfeited to the opponent if the bidder bids $20. Should ensure compliance and I get the maximum $9 EV, plus I don't have to do any math.
@Markd3152 жыл бұрын
But yes looking over the other respondents answer their msne solution looks correct.
@Gametheory1012 жыл бұрын
This is why I like studying international relations. Limited to no external enforcement!
@jvgama2 жыл бұрын
There should be third equilibrium where you choose to bid 10$ with a 40% probability (and 20$ with a 60% probability), if you expect the other player to bid 10$ with an 80% probability (and bid 20$ with 20% probability), if I am not mistaken. Interesting puzzle, as always. In this case, talk is not cheap: if agents can coordinate to choose the best outcome (which happens to be the best equilibrium for them as well), why wouldn't they do it? Reality is messy.
@Gametheory1012 жыл бұрын
That's right. Per the odd rule ( kzbin.info/www/bejne/iJm2kqRvbL6dmKM ), there is a third equilibrium, and it is in mixed strategies.
@igaviotis-tblcube8722 жыл бұрын
The mixed strategy equilibrium (row player offering 10$ with probability 40%; column player offering 10$ with probability 80%) seems reasonable, because it takes into account the 'valuations' (row player's 28$; column player's 24$). In general, if row player valued the book at a$ and column player at b$, both in [21,29], then row player would give 10$ with probability b/10-2 and column player would give 10$ with probability a/10-2. What strikes me is that the probability for each player's offer, only depends on the other player's valuation.
@Gametheory1012 жыл бұрын
Yep! And that's a general property of mixed strategies: you need to choose a mixture that induces indifference from your opponent. Thus, small changes to your payoffs do not change your strategy, only changes to your opponent's. (Large changes to your payoffs can give you a dominant strategy, hence the "small" caveat.)
@dictatorofcanada4238 Жыл бұрын
“Eh, I’ll take a loss of $2 to give me a better chance to get the book. $2 isn’t that much.”
@gh-sb1dy9 ай бұрын
hi who decides the actual prices of a stock ?for example if news comes out do any owners of the stock decide and can freely ask what ever they want for the stock which drives the stock price up? or is there some kind of rule or term they must follow to raise the price of a stock? who decides these things? OR is price determined by strict supply demand rules by the float/ outstanding shares available?
@sinecurve99992 жыл бұрын
I wonder if anyone really values that textbook at $28! #UnexpectedFactorial
@Gametheory1012 жыл бұрын
I sure hope so---even if no (hopefully) has ever actually paid that much for it. (MSRP is half that.)
@stevekerp1 Жыл бұрын
I don't think you can talk about "net profit" until the new owner sells the book, and then it's only worth what someone else is willing to pay for it. So if I "value" the book at $24, that's essentially meaningless. Do I want the book, or am I buying it because I think someone will show up who wants it more than I do? I'm sure this is illustrating something useful about game theory, but the story does not seem to make any game theory principle clearer to me.