People often ask, ““. Previous answers to this question often included the noun phrase “world computer”, but , it’s been difficult to answer this question at a more abstract level. I offer a potential answer to this question. I propose that,
is an unprecedented arena for playing cooperative games.
and moreover,
enables powerful economic vehicles we don’t yet understand.
, the original and most widely used branch of game theory, assumes the absence of an external authority to enforce rules. Fundamentally, I claim that the constitutes an incorruptible, omnipresent, external judge that no matter the game is always available to enforce agreements among players. This implies that , in theory, could turn any non-cooperative game into a cooperative game.
The transmogrification from non-cooperative to cooperative games is achieved by a technique we term Game Warping defined as using transparent, triggerable, unstoppable burns and on-chain side-payments to move game-theoretic equilibria as well as to create new player actions. Game Warping adds a new layer on top of old games to make cooperation the Rational choice.
Example 1: The Prisoner’s Dilemma
The most well-known problem in game theory is the —it is the quintessential example of a in which the Rational strategy puts players into the worst possible state. Under , I kid you not, the Prisoner’s Dilemma becomes a cooperative game. Say players A and B want to do something naughty. But before they commit their , they each deposit one million dollars (valued at 1000 utility points) into a smart-contract which states, “If I publish a defect message, my million dollars gets destroyed.” Now that the smart-contract is in place, as long as the don’t offer more than a million dollars to defect, Rational prisoners will choose to cooperate.
In the original Prisoner’s Dilemma, Rational players will both defect. But after the pay-off matrix has been warped to have a new equilibrium, Rational players will both cooperate. See below,
For inspiration, this includes carbon-emissions, sports doping, tragedy of the commons, and international weapons buildup. Could have something to offer these areas? It seems plausible.
Example 2: The Stag Hunt
The is a canonical model of cooperation. The game posits two hunters choosing to hunt either Stag or Rabbit. The greatest pay-off is when both players hunt Stag (successfully hunting stag requires both hunters working together). But hunting stag is also the riskier strategy, because if the other hunter goes Rabbit, the hunter who went Stag gets nothing — the safe option is the guaranteed pay-off from hunting rabbit.
The desired warping is the same as the Prisoner’s Dilemma. Each hunter deposits a large sum (worth 1000 utility points), that is burned if the hunter hunts Rabbit.
Example 3: The Chicken Game
In addition to warping games for collective benefit, a player can also game-warp to gain a personal advantage. We illustrate this with the game of . In this game, there are two players A and B and two actions, Swerve and Straight. The players aim to choose opposite actions. Chicken is a game where by removing one of your own options (Swerve), the other player’s Rational response is to your benefit. This can be done by making a large on-chain deposit which burns if you Swerve, thus assuring the other player that you would never Swerve. This is the equivalent of “publicly throwing away the steering wheel.”
Chicken has two equilibria: [Straight,Swerve] and [Swerve,Straight]. But after the warp, the only remaining equilibrium is [Straight,Swerve], netting you (player A) the maximum pay-off. In an world, Chicken becomes a race to publicly toss out one’s own steering wheel.
Example 4: Warping Other Players’ Games
Not limited to profiting from warping one’s own games, one could even profit by threatening to warp games you’re not even party to. Such extortion is obviously not endorsed, but we include it as a ramification of smart-contract technology. Consider the situation from from & , where if a third player C knows players A and B are about to play a game (and their pay-off matrix). With , C can create a smart-contract in clear view of players A and B. This newly created contract states that unless A pays the contract, the contract will send a large payment to B conditional on B performing a rivalrous action against A. In essence, player C is extorting player A by credibly threatening to incentivize B to act rivalrous against A.
More concretely, consider the case below. Player A has actions Up/Down and player B has actions Left/Right. Initially, they both so desperately desire to occupy (Up, Left) in a very positive-sum interaction of ten utility points. However, an external player C recognizes the game about to be played and instantiates a smart-contract to extort $5000 (worth 5 utility points) from player A. If A does not pay the contract, the contract will pay B a hefty $100,000 (worth 100 utility points) to choose Right. Once Player sees the smart-contract, A is faced with the choice between two worse options — Composite Game I or Composite Game II. Unfortunately for player A, the Rational choice Composite Game II, and A pays the extortion fee.
One of the most surprising aspects of game-warping is that someone making a credible promise to pay can often change the Rational strategy (and thus often the outcome of the game) without ever actually having to pay — if everyone plays Rationally, the game can be influenced for free!
Caveat. payments and burns can only be triggered by an on-chain event. This is clearly a limitation — for example, in the prisoner’s dilemma, if a prisoner could defect without it being broadcast on-chain, the player sidesteps the million-dollar burn. The relevance of side-channel (off-chain) communication will vary case-by-case. But the fewer off-chain interactions between players, the more likely the game can be successfully warped. The biggest contributions to this area will be discovering the exact property that games must have to ensure all relevant player actions will be broadcast on-chain.
An additional caveat is that, for game-warping to succeed for individual gain, the recipient players must discover the warp has been performed. This limitation on anti-social may turn out to be a social blessing.
What does change? Technically speaking, game-warping doesn’t require smart-contracts. But (or another smart-contract platform) makes game-warping vastly more practical by providing a mechanistic, all-seeing, expedient judge. For example, it’s difficult to find an arbiter who impartially renders verdicts on the scale of billions of dollars, much less nation-states.
Ramifications. This framework provides a process for generating startups. For example one could:
- Go through a .
- Enumerate all of the common non-cooperative games.
- See how many of those games could cooperation, via conditional payouts or deposit burns, yield a superior equilibrium than the original Nash equilibria.
- Discover prominent industries where these games appear.
- For each industry, determine if the player actions could be made into on-chain events. If so,
- Submit a startup proposal to become a .
Seriously, steal this idea.
Special thanks: This game-warping , , and for our joint research developing game-warping and feedback on drafts.
Published at Fri, 29 Mar 2019 08:00:50 +0000
