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According to the following requirements (Source: Playing for Real by Ken Binmore):

  1. The game is presented to the subjects in a user-friendly way that makes it easy for them to understand what is going on.
  2. Adequate cash incentives are provided, so that the subjects have good reason to pay attention to the problem with which they are faced.
  3. Sufficient time is made available for trial-and-error learning. This means that the subjects must be allowed to play the game repeatedly, against new opponents each time.

What kind of game we can give as an example that doesn't fit with rule 1, a game that doesn't fit with rule 2 and a game that doesn't fit with rule 3.

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    $\begingroup$ Editing tips: Use block quotes (by adding the > symbol to a paragraph) for extended quotation instead of a code block. $\endgroup$
    – Herr K.
    Jul 26, 2022 at 15:17

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These so-called "Binmore rules" are criteria for "a favorable experimental environment for game theory" (Binmore 2007, emphasis mine). They are not requirements on games per se, but rather on the experimental adaptation of games. The satisfaction of these rules is a matter of degree (and sometimes of taste).

Take the classical Prisoner's Dilemma game (PD) as an example. I'll talk about how to incorporate the three rules in designing an experiment involving this game.

Rule 1 is about presentation. That is, the game needs to be presented to subjects in an easily understandable manner so as to ensure that the experimenter observes deliberated choices rather than confusion. For example, a purely verbal description of PD would be less "user-friendly" than say a tabular presentation.

Rule 2 is about stakes. In order for choices observed in the experiment to be meaningful, the subjects have to be given an incentive that dominates other considerations that they bring from outside the experiment (e.g. social norms, rivalry, altruism, boredom, confusion, etc.). Not only does this mean that subjects should be compensated for their time, but they should also be paid based on the outcome of the games they play in the experiment. Moreover, the payment should vary noticeably between "good" and "bad" outcomes. In a PD experiment, the matrix on the left below would be less salient than the one on the right (numbers in dollars). $$\begin{array}{|c|c|c|} \hline &C&D \\\hline C&3, 3&2, 4\\\hline D&4, 2&1, 1\\\hline \end{array}\quad\quad\quad \begin{array}{|c|c|c|} \hline &C&D \\\hline C&3, 3&1, 5\\\hline D&5, 1&0.5, 0.5.\\\hline \end{array} $$

Rule 3 complements Rule 1 to ensure understanding. Repetitions help subjects gain experience and adapt to the role/environment, as comprehension is often gained through practice. In a PD experiment (designed to study one-shot behavior), a one-round procedure (i.e. each subject plays PD only once) would be less useful than repeated play with perfect stranger (re-)matching (i.e. each subject plays the same PD multiple times, each time with a different person).

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  • $\begingroup$ Thanks! One question: I don't understand the 3rd rule, do you have examples of games in real life that the rule doesn't fit with, except of the PD? $\endgroup$ Jul 26, 2022 at 16:14
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    $\begingroup$ @PedroGómez: Here's another way of looking at Rule 3: If one wants to study a game experimentally, then they need to give the subjects enough opportunity to get familiar with the game first. That's why modern experimental designs often include features like practice rounds, paid quiz on instructions, etc. to ensure that subjects have sufficient understanding of what they need to do before letting them play "for real". $\endgroup$
    – Herr K.
    Jul 26, 2022 at 16:48
  • $\begingroup$ Hello Dear @Herr K. you are explained so good. Can you please look at my question as well? I only want you to check for payoffs in the game. I am confused too much. Thank you economics.stackexchange.com/questions/52455/… $\endgroup$
    – studentp
    Aug 23, 2022 at 20:00

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