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    Entries in game theory (4)

    Wednesday
    18Nov2009

    Usman Haque (developer of Pachube) on the future of 'The Internet of  Things'

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    "One of the challenges we're facing is the question of what is private and what is public. How do you give people control over their privacy? Yes there's the technical question of getting your fridge to talk to the supermarket, but the more challenging question is: what is the interface for allowing people to determine what the fridge says?"

    In addition to the dead simple Pachube platform that allows developers to connect sensors from things in real space to outputs in the digital world (and back to real space applications), Haque has been involved in a fascinating number of other projects that explore how we interact with our environment.

    Of note is Natural Fuse, a collaboration with Nitpak Samsen (who, incidentally, I mentioned earlier for his conceptual control panels). This network of plants and power outlets limits the output of power by how much the plants can counter the resulting carbon footprint. Very game theory-esque.

    If you're looking to be inspired by great thinking with respect to being aware of our impact on the envronment, I definitely recommend http://www.haque.co.uk and http://www.dotmancando.info.

    Posted via email from Kyle's posterous

    Wednesday
    09Sep2009

    Utility and cooperation in Prisoner's Dilemmas: dollars and donuts edition

    Last week I attempted to pit two volunteers against each other in a staple Prisoner's Dilemma, but my ulterior motives (wanting to give away a book) threw a wrench in the plan, leaving one participant with a free book and a good charity (see: SafePlace) $10 better off. Wanting to truly recreate a "cooperate vs defect" experience, I decided to take a box of donuts down to the local university armed with a sign that read "FREE DONUT (maybe)."

    Since my intent was to garner a variety of experiences, there ended up being a few variations of the decision-making game I had in mind. The first group to approach me and my sign was presented with the following rules:

    1) In order to win a free donut, you must have and be willing to lose a dollar.

    2) To play the game, you must make each separately make a decision between spending the dollar to receive a donut in exchange, or keeping the dollar to get a donut for free at the expense of the other player.

    3) If one player decides to spend their dollar but the other decides to keep their dollar,  the person who kept their dollar gets a donut for free, while the person who decides to spend the dollar gets nothing. If both players make the decision to spend the dollar, then both dollars are returned AND both players get a donut. If both decide to keep the dollar, however, no one gets anything.

    This sounded about right in my head. I had each player turn their backs to each other, make a decision by either placing the dollar or not in their right hand (placing the dollar in the right hand indicates the 'spend' decision, keeping the dollar in the left hand indicates a 'keep' decision), then turn back around and display their choice in dramatic Rock, Paper, Scissors fashion. As it turned out, the result was that both players decided to spend their dollar, and as promised I gave each a free donut.

    After some thought, I realized that the decision I presented them with looks like this:

    When looking at these diagrams you want to pay attention to a couple of things. First: individual utility. 

    The way it goes in theory is that each player judges the utility of each outcome (represented here by the numbers below each face) and makes their final decision based on whether taking the alternative would yield more utility. Player 1 compares alternative outcomes laterally (relative to player 2's decisions) while player 2 compares thier own potential outcomes vertically. This leads to the ideal outcome on an individual level. Here in this example, there is no functional benefit of switching from the 'keep' option to the 'pay' option; they are both equally beneficial if the other player pays, and you're worse off in the case where the other player keeps.

    So going back to the above decision matrix, it's not surprising that this first group ended with a keep/keep 'nothing happens' result. Not very exciting. (Although I did end up giving them free donuts for participating.)

    In the end I wanted to orchestrate that contrast between the 'best decision' result and the 'having to settle for something less-than-optimal, but in the interest of being safe decision' result. The second thing that's important to pay attention to is the overall utility, which points at what that 'best decision' would be. By adding the utility of both players' results in each scenario, you can identify which scenario represents what is 'best' overall. In the traditional Prisoner's Dilemma diagram (below), you can see that cooperating leads to the most overall utility (14), although individual utility draws each layer to the least optimal result (overall utility of both defecting: 8) (indeed, this is the crux of the dilemma).

     

    I approached the next groups with the same prospect, but instead of having the players potentially spend a dollar of thier own, I gave each one to use for the game. If they both keep the dollar, they both end up a dollar richer. If they both spend, they each get a free donut*. But if one spends and the other keeps, the keeper has to give the dollar back, while the spender keeps their dollar AND gets a donut. The resulting matrix is below:

     

    These scenarios were interesting. Applying our game theory reasoning, the result should lean toward spend/spend. But more often than not, I got spend/keep - why? (This is an hilarious result, by the way. One girl, expecting her friend to cooperate for the sake of free donuts, had quite a reaction to his decision to keep the dollar. I had to retrieve my dollar from the ground, after she threw it in the face of her "friend.")

    The 'why?' is in the utility. As noted in the asterisk above, *I had to emphasize "free," with the justification that I was giving them a dollar. Which is fine for those  who get the same utility from both a dollar and a donut, but:

    1) if a donut is only worth $0.25 to you, the resulting matrix changes entirely, and

    2) even if a donut is worth $1 to you, given that you start out with a free dollar, you have to spend that dollar to get a donut. Loss aversion (see: Business Built on Loss Aversion) weighs in heavily here.

    The ideal situation is relatively straightforward hybrid of my earlier attempts, but I ran out of donuts before being able to test it. The decision matrix simply needs to look like this:

     

    To get here, each player needs to cooperate with the other by paying a dollar (from their own pocket) for the sake of both getting a free donut (the dollar would be returned). The alternative is to not pay; if neither player pays a dollar, no one gets anything. In the split result, the player who pays loses their dollar, while the person who keeps gets a donut AND the other player's dollar.

    Again, the expected result is the 'no result' keep/keep, but at least this time they get there in the face of the win/win '(truly) free donuts' result.

     

    [What would your decisions be??]

    Tuesday
    08Sep2009

    a quick decision-making game / crash course in Orchestrating Prisoner's Dilemmas

    Since I was one of the lucky 500 to get a free signed copy of Hugh MacLeod's Ignore Everybody (And 39 Other Keys to Creativity), I've had an extra one sitting around from my original purchase. Realizing there's some fun to be had here, instead of just giving my extra copy away I decided to play a little decision-making game by drafting a couple of unwitting volunteers for something of a social experiment. If nothing else, the book was going to serve me at least a little entertainment.

    The only requirement for my two volunteers before commitment was that they 1) wanted the book, and 2) were okay with the possibility of donating a few bucks ($10) to charity as a result of playing the game. Once they were locked in I explained the rules:

    The only thing each player needed to do was make a decision between two options:

    Option A - Ask to get the book for free

    Option B - Donate $10 to a charity of their choice and send me an email confirmation

    Since both players chose between two options (at the same time, and without knowing who their competitor was), I defined the four possible results of the game:

    "Scenario 1 - both players email me with a receipt verifying their donation; I match the $10 by emailing each player with my own verification of $5 donation to the same charities. (medium win/medium win)

    Scenario 2 - Player A asks for the book, Player B donates to charity. Player A gets the book for free, Player B loses out on the cost of donation. (win big/lose big)

    Scenario 3 - Player B asks for the book, Player A donates to charity. Player B gets the book for free, Player A loses out on the cost of donation. (win big/lose big)

    Scenario 4 - Both players ask for the book. No one gets anything. (lose/lose)"

    Originally my intent was to both give away my free copy and simultaneously orchestrate something of a prisoner's dilemma, that old game theory staple. Of course, the essence of a prisoner's dilemma is that each participant has to chose between cooperation with the other (at the risk of losing out big if the other defects), or defecting for a big reward; if both cooperate, each participant is rewarded moderately (best possible outcome), but if both defect, both face an undesired outcome. The dilemma is that without any certainty of the other player's decision, when each player evaluates the individual utility of potential outcomes of either choice, there is always more utility in either switching to or staying with the 'defect' option - and since both players evaluate the situation accordingly, they both end up in the lose/lose undesired outcome. Allow me to illustrate:

    Prisoner's Dilemma

    Have you pointed out yet where there's a couple of critical non-prisoner's-dilemma things going in the case of this book experiment? For one, there's not exactly a true "cooperate or defect" dynamic here. The "donate" option isn't inherently a bad thing, in the sense that it's likely to act as a rewarding option for the more charitable among us. And on top of that there's not really any sense of betraying the other player if you donate anyway. The decision ends up being not so much "should I cooperate or defect," but something closer to "which one do I like more: free book, or giving to charity?". With the "win big/lose big" designators I tried to describe the situation as closely to "you have the potential to be screwed over by the other player if they choose the book and you don't" as possible, but ultimately I don't think too many people would be all that discouraged hearing "sorry, a stranger got a free book while you gave money to a good cause (of your choice)." 

    Which, by the way, is what ended up happening. Player 1 Libby Anderson gave $10 to SafePlace, a woman's shelter she's been working with alongside Planning For Good in Austin, while book-loving Player 2 Rebecca Stein asked for and got the free book. Interestingly enough though, Libby noted that after missing her response deadline by a week, she opted to redeem her guilt via charitable donation. Meanwhile, Rebecca remarked that it may have in fact been the pressure of the 24 hour turnaround time that drove her selfish type response. But no worries, Rebecca has offered to pass on the book to Libby once she's done. Everyone's a winner. Even from my perspective: I got to give my book away, and got someone to donate a few bucks to a good cause. You guys rock, as always. 

    I stepped back and considered this part one of my entry-level course in Orchestrating Prisoner's Dilemmas, and started cooking up other ways to get at that elusive "cooperate vs defect" dynamic. Would my next experiment, making use of college students, dollars and donuts, hit the mark??? Stay tuned to find out.

     

    Monday
    24Aug2009

    stages, game theory's homo economicus, and time orientation

    Right now I'm thinking of Kubler-Ross and her set of responses to loss. I'm wondering: do you think that given an awareness and understanding of these states, being aware of any given state you happen to be in diminishes it's importance? What I'm trying to get at applies to anything that progresses in stages, and in the case of Kubler-Ross it's the following question: if you're actively aware of being in the anger phase, is your anger less important knowing that it will eventually subside to acceptance?

    In a strange way, I'm reminded of the Free Rider Dilemma that appears in game theory. Here the individual must decide whether or not to contribute a donation to the development of a shared resource, where if the sum of everyone's contributions reaches a certain threshold then everyone benefits from the resource (say, for example, that a community center can be built with the pooled money), but if the sum of everyone's contributions fails to meet that threshold then no one benefits from the resource because it fails to manifest (and individual contributions are lost). Where perfect knowledge exists, the only case where it rationally makes sense to donate is when your donation will tip the scale (see Len Fisher's example matrix here from his book Rock, Paper, Scissors). In other words, the only donation that makes sense is the last one.

    When it comes to things that progress in stages, I'm wondering if the same idea applies: the only stage that matters is the last one. Note that in the reality of the Free Rider Dilemma, perfect knowledge almost never exists (every participant knows that their contribution only make sense if theirs is the one that tips the scale, but everyone makes their contribution at the same time, or at least w/o the knowledge of others), but in the case of development in known stages, perfect knowledge is in fact the very problem.

    A couple of thoughts come to mind that address the question. First, this analysis is very close to the idea of backward induction that makes rational and logical sense, and is consistently proven mathematically as the best strategy in a number of decision-making games. Backward induction essentially operates with perfect knowledge of the final stage of a process, and works in reverse to determine an optimal strategy. It leads to counterintuitive but mathematically and logically sound strategy of defecting on the first round of the Centipede game (where a pot of money to be split equally is passed back and forth between two players, increasing in value each time passed, but at any point any player with the pot in hand may defect and take a 60% majority) and the similarly sound strategy of asking for the least amount of reimbursement for lost goods in the Traveler's Dilemma.

    But these strategies are highly counterintuitive, and not surprisingly are rarely replicated in actual simulations. So the second thing comes to mind is Phillip Zimbardo's thoughts on time-orientation:

    In short, he compares the happiness and success of people with varying focuses on the past, present, and future, concluding that there's some optimal blend of sacrificing the rewards of one for the rewards of the others (think: instant vs delayed gratification). And I think that ties a lot of these problems together. Were we all perfectly future orientated, yeah the homo economicus strategies rational game theory predicts would manifest themselves in real life. And knowing that acceptance is inevitable would make things like anger and fear meaningless and even more irrational (read: in more than just the sense that they are emotions, in the even greater sense that they ultimately wouldn't matter).

    But clearly that's not really the best path to success/happiness. That path lies in a blend of future, present and past orientations, where things in the present ultimately do matter and should be appreciated, indulged in, loved, hated, and experienced. Focusing solely on the future, simply enough, means overlooking the meaningfulness of the present. 

    (interestingly problem: it means overlooking the past, too. In fact, this might also be the solution to another problem I've been thinking on: the similarly "sound/rational" strategy of ignoring sunk costs. Another time; too much for one post.)

    What's your time-orientation strategy??