Indifference curve analysis aims
to model how individuals consume, specifically looking at preferences and
substitutions between goods when price and income vary. An indifference curve
is a line joining all of the bundles of two goods that a consumer is
indifferent between. An indifference map combines all the indifference curves
of an individual and once the individuals budget constraint has been added it
can be used to find the maximum utility of the consumer- which is the best
affordable bundle (i.e the highest indifference curve reachable by the budget
constraint) Prior to indifference curve analysis Marshallian utility theory was
used to model how individuals consume, but indifference curve analysis proved
superior in a number of ways. A good example of this as well as the
applicability of indifference curve analysis is it explains the law of demand better
than utility theory. Indifference curve analysis allows us to separate the
effect on demand of a price change into two individual components-the
substitution effect and the income effect. The substitution effect is the
component of total effect that comes from the change in relative attractiveness
of other goods after a change in price of a good, while the income effect is
the component of the total effect that comes from the change in relative
purchasing power. Being able to separate the two distinct effects has become
important in a number of situations. For example, when attempting to model the
supply of labour in an industry/economy one would assume that as wages
increase, labour supply will increase proportionately. However, it is commonly
observed that this is only true up to a certain point, then it decreases as
wages continue increasing. Indifference curve analysis allows us to explain
this by breaking down the two observed relationships into the substitution and
income effect. As wages increase, the demand for leisure time decreases due to
the substitution effect- the cost of leisure time is wages given up, the cost
of leisure increases with wages, thus demand falls. Leisure time is a normal
good however, so when wages increase income, the demand for leisure time
increases due to the income effect. Indifference curve analysis also allows us
to see that at low wage levels the substitution effect dominates, while at high
wage levels the income effect dominates. This explains the backward bending supply
of labour and allows policy makers to tailor policy towards certain outcomes or
groups of individuals based on income levels. 

The limitations of indifference
curve analysis are largely related to it being a rigid model, while the thing
its modelling (consumption) is very much dynamic and indifference curve
analysis doesn’t take enough of the contributing factors into account. For
example, indifference curve analysis considers the relationship between two
commodities but in the modern market there are many variety’s, substitute and
complementary goods that will likely have an impact on the consumption of the
commodities in question but aren’t included in the analysis. Similarly, ‘The
theory of games and economic behaviour’ credit risk and uncertainty as major
factors affecting the way individuals consume, and go as far as to claim
indifference curve analysis has no uses if risk and uncertainty are present,
which they usually are. Furthermore, the axioms of preference upon which the
analysis is based are also very rigid, particularly transitivity. However,
consumers are complicated and many different elements influence and change
their preferences constantly and indifference curve analysis does not consider
these changing preferences at all as it holds preferences constant.

Game theory analyses multi-person decision
making issues where the outcome of a participant’s choice of action
depends critically on the actions of other participants. There are many
variations and applications of game theory as well as there being many
different types of games. Non-cooperative games are games where each player has
only their best interests in mind so there is no collusion. If the game is
finite, there is always at least one Nash Equilibrium point which means no
player can obtain a higher payoff by using a different strategy. Nash
equilibrium is a strong solution concept and has many applications in real life
in pure      non-cooperative games such
as poker.  As there can only be one
winner, no one in poker is likely to be cooperating and everyone will be using
their dominant strategy, so a Nash equilibrium is the outcome. However, one of
the main limitations of this that John Nash discussed himself in his
non-cooperative games paper (1951) is as you add in more players, more decks
and other rules and factors that change the parameters of the game, the
mathematics needed to find the Nash equilibrium gets more complex and is likely
to need an approximate computational model. Another application of game theory
and Nash equilibriums is shown by Hotelling’s game. Two vendors are on a beach that stretches the 0-1 interval,
customers are uniformly distributed along that interval, the vendors
simultaneously select a position. Customers go to the closest vendor and split
themselves evenly if the vendors choose an identical position. Although
traditional business logic would dictate you should be as far from your
competitor as possible, both vendors guarantee themselves half the customers if
they go to the median (.5) position, and cannot gain anymore by deviating from
this strategy. This theory has a wide range of applications, such as the
location problems discussed above, or in a game between two political
candidates competing for votes along a spectrum of political views. The best place
for them both to position themselves is the centre of the spectrum as they
guarantee themselves half the votes. However, much like with the poker
applications, as the n number of players increases the median voter theorem is
much less prevalent. Furthermore, for games with odd amounts of players the
strategies and solutions get much more complex, limiting the effectiveness of
the model.

Game
theory can also be applied in cases of cooperative games such as the formation
of cartels. Cartels are formed when a group of firms decide to collude with one
another and pick the same strategy in order to fix higher prices to raise
profits- aiming to reach the level of output and price that a monopoly would
provide. The first limitation of this comes in the forming of the cartel. If
there are fixed set up costs for the cartel it will only be set up if the
expected profit gains from the cartel exceed the costs. Furthermore, if the
market is concentrated to a small number of firms, collusion is much easier for
two key reasons. Firstly, with less firms to collude with, the issues
associated with the organisation of the cartel are minimised. Secondly, if
there are less existing firms in the market, the potential profit the cartel
will split will be higher so there is more incentive to collude and conversely
more firms mean less profit. This means that cartels are largely limited to
industries that are concentrated in terms of how many firms are in the
industry. The second limitation to cooperative games was put forward by Stigler
(1964) which is that cartels will inevitably fail due to temptation to cheat on
the cartel agreement by lowering prices. The increased cartel prices mean each
firm is producing at a point where price>marginal costs, thus each firm
faces a prisoner’s dilemma as they could make more profit by reducing prices
and increasing outputs. The monitoring and punishing of these infractions is
very difficult and a big limitation for cartels, it usually leads to price wars
which is traditionally seen as the cartel breaking up. However, Green
and Porter (1984) argue that price wars is actually the cartel restabilising
itself, and by reducing the incentive to cheat in future the cartel makes
itself more sustainable. This is in itself another application of game theory,
as when firms are producing away from their profit maximising output (price=marginal
cost) they face a prisoner’s dilemma. Price wars is a way of reducing the
appeal of the other strategy and ensuring no one cheats on the agreement. The
biggest threat faced by cartels is new entry into the market, and is also the
hardest for them to overcome. When new firms enter the market, supply is
increased which drives the price down, and reduces the cartels potential
profit, which increases the incentive for firms to cheat on the agreement. If
the cartel was to try and start creating barriers to entry they would likely
conflict with anti-competition laws, or at least make authorities more aware of
their activities-which would be a major issue in most countries as collusion is
illegal in many places across the world. Ultimately, economists are split in
regard to the sustainability and success of cartels, and a large reason for
this is the lack of information on a lot of cartels as they are often illegal.