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ity (best close concept to rationality of game theory)
and heuristics people use to reason in strategic situa-
tions. For example we can note surveys of Crawford
et al.; Mauersberger and Nagel (Crawford et al., 2013;
Mauersberger and Nagel, 2018). Also there is com-
prehensive description of the field of behavioral game
theory by Camerer (Camerer, 2011).
Also we can note work of Gill and Prowse (Gill
and Prowse, 2016), where participants were tested on
cognitive abilities and character skills before the ex-
periments. Then authors perform statistical analysis
to understand the impact of such characteristics on the
quality of making strategic decisions (using p-beauty
contest game with multiple rounds). In more recent
work of Fe et al. (Fe et al., 2019) even more elabo-
rate experiments are presented. It is interesting that in
the mentioned paper experiments are very strict and
rigorous (as close to laboratory purity as possible) in
contrast to games, played in our research. But in the
end of the day the results are not differ very much.
The guessing games are notable part of research
because of their simplicity for players and easy anal-
ysis of rules from game theoretic prospective. In
this paper we present results of games played during
2018–2020 years in series of scientific popular lec-
tures. The audience of these lectures was quite hetero-
geneous, but we can distinguish three main groups:
• kids (strong mathematical schools, ordinary
schools, alternative education schools);
• students (bachelor and master levels);
• mixed adults with almost any background;
• businessmen;
• participants of Data Science School.
We propose framework of four different games,
each presenting one idea or concept of game theory.
These games were introduced to people with no prior
knowledge (at least in vast majority) about the the-
ory. From the other hand, games have simple formu-
lation and clear winning rules, which makes them in-
tuitively understandable even for kids. This makes
these games perfect choice to test ability of strate-
gic thinking and investigate process of understanding
of complex concepts during the play, with immediate
application to the game. This dual learning, as we
can name it, shows how players try-and-learn in real
conditions and react to challenges of interaction with
other strategic players.
1.1 Game Theory Definitions
We will consider games in strategic or normal form in
non-cooperative setup. A non-cooperativeness here
does not imply that the players do not cooperate, but
it means that any cooperation must be self-enforcing
without any coordination among the players. Strict
definition is as follows.
A non-cooperative game in strategic (or normal)
form is a triplet G = {N , {S
i
}
i=∈N
, {u
i
}
i∈N
},
where:
• N is a finite set of players, N = {1, . . . , N};
• S
i
is the set of admissible strategies for player i;
• u
i
: S −→ R is the utility (payoff) function for
player i, with S = {S
1
×·· ·×S
N
} (Cartesian prod-
uct of the strategy sets).
A game is said to be static if the players take their
actions only once, independently of each other. In
some sense, a static game is a game without any no-
tion of time, where no player has any knowledge of
the decisions taken by the other players. Even though,
in practice, the players may have made their strate-
gic choices at different points in time, a game would
still be considered static if no player has any informa-
tion on the decisions of others. In contrast, a dynamic
game is one where the players have some (full or im-
perfect) information about each others’ choices and
can act more than once.
Summarizing, these are games where time has a
central role in the decision-making. When dealing
with dynamic games, the choices of each player are
generally dependent on some available information.
There is a difference between the notion of an action
and a strategy. To avoid confusions, we will define a
strategy as a mapping from the information available
to a player to the action set of this player.
Based on the assumption that all players are ra-
tional, the players try to maximize their payoffs
when responding to other players’ strategies. Gen-
erally speaking, final result is determined by non-
cooperative maximization of integrated utility. In
this regard, the most accepted solution concept for a
non-cooperative game is that of a Nash equilibrium,
introduced by John F. Nash. Loosely speaking, a
Nash equilibrium is a state of a non-cooperative game
where no player can improve its utility by changing
its strategy, if the other players maintain their cur-
rent strategies. Of course players use also informa-
tion and beliefs about other players, so we can say,
that (in Nash equilibrium ) beliefs and incentives are
important to understand why players choose strategies
in real situations. Formally, when dealing with pure
strategies, i.e., deterministic choices by the players,
the Nash equilibrium is defined as follows:
A pure-strategy Nash equilibrium (NE) of a non-
cooperative game G is a strategy profile s
0
∈ S such
that for all i ∈ N we have the following inequality:
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